A hybrid modeling approach for option pricing
NASA Astrophysics Data System (ADS)
Hajizadeh, Ehsan; Seifi, Abbas
2011-11-01
The complexity of option pricing has led many researchers to develop sophisticated models for such purposes. The commonly used Black-Scholes model suffers from a number of limitations. One of these limitations is the assumption that the underlying probability distribution is lognormal and this is so controversial. We propose a couple of hybrid models to reduce these limitations and enhance the ability of option pricing. The key input to option pricing model is volatility. In this paper, we use three popular GARCH type model for estimating volatility. Then, we develop two non-parametric models based on neural networks and neuro-fuzzy networks to price call options for S&P 500 index. We compare the results with those of Black-Scholes model and show that both neural network and neuro-fuzzy network models outperform Black-Scholes model. Furthermore, comparing the neural network and neuro-fuzzy approaches, we observe that for at-the-money options, neural network model performs better and for both in-the-money and an out-of-the money option, neuro-fuzzy model provides better results.
ERIC Educational Resources Information Center
Tenopir, Carol
1998-01-01
Presents results of a recent survey of over 100 public and academic libraries about pricing options from online companies. Most options fall into three categories: pay-as-you-go, fixed-rate, and user-based. Results are discussed separately for public and academic libraries and for consortial discounts. Trends in pricing options preferred by…
Modeling of certain problems in financial mathematics: Spread option pricing
NASA Astrophysics Data System (ADS)
Khorev, K. P.
2007-04-01
The problem of valuating exotic options, namely, the option on the spread between two forward interest rates is considered. The price of the option is derived under the assumption that the dynamics of debt instruments and the interest rates are described by the Heath-Jarrow-Morton model. The parameters of the model are estimated, and the price of the option is numerically computed based on Russian bond market data.
Fluctuation in option pricing using cellular automata based market models
NASA Astrophysics Data System (ADS)
Gao, Yuying; Beni, Gerardo
2005-05-01
A new agent-based Cellular Automaton (CA) computational algorithm for option pricing is proposed. CAs have been extensively used in modeling complex dynamical systems but not in modeling option prices. Compared with traditional tools, which rely on guessing volatilities to calculate option prices, the CA model is directly addressing market mechanisms and simulates price fluctuation from aggregation of actions made by interacting individual market makers in a large population. This paper explores whether CA models can provide reasonable good answers to pricing European options. The Black-Scholes model and the Binomial Tree model are used for comparison. Comparison reveals that CA models perform reasonably well in pricing options, reproducing overall characteristics of random walk based model, while at the same time providing plausible results for the 'fat-tail' phenomenon observed in many markets. We also show that the binomial tree model can be obtained from a CA rule. Thus, CA models are suitable tools to generalize the standard theories of option pricing.
Exponential model for option prices: Application to the Brazilian market
NASA Astrophysics Data System (ADS)
Ramos, Antônio M. T.; Carvalho, J. A.; Vasconcelos, G. L.
2016-03-01
In this paper we report an empirical analysis of the Ibovespa index of the São Paulo Stock Exchange and its respective option contracts. We compare the empirical data on the Ibovespa options with two option pricing models, namely the standard Black-Scholes model and an empirical model that assumes that the returns are exponentially distributed. It is found that at times near the option expiration date the exponential model performs better than the Black-Scholes model, in the sense that it fits the empirical data better than does the latter model.
Chalasani, P.; Saias, I.; Jha, S.
1996-04-08
As increasingly large volumes of sophisticated options (called derivative securities) are traded in world financial markets, determining a fair price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs. In this paper the authors show that pricing an arbitrary path-dependent option is {number_sign}-P hard. They show that certain types f path-dependent options can be valued exactly in polynomial time. Asian options are path-dependent options that are particularly hard to price, and for these they design deterministic polynomial-time approximate algorithms. They show that the value of a perpetual American put option (which can be computed in constant time) is in many cases a good approximation to the value of an otherwise identical n-period American put option. In contrast to Monte Carlo methods, the algorithms have guaranteed error bounds that are polynormally small (and in some cases exponentially small) in the maturity n. For the error analysis they derive large-deviation results for random walks that may be of independent interest.
Option pricing formulas based on a non-Gaussian stock price model.
Borland, Lisa
2002-08-26
Options are financial instruments that depend on the underlying stock. We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter q. A generalized form of the Black-Scholes (BS) partial differential equation and some closed-form solutions are obtained. The standard BS equation (q=1) which is used by economists to calculate option prices requires multiple values of the stock volatility (known as the volatility smile). Using q=1.5 which well models the empirical distribution of returns, we get a good description of option prices using a single volatility. PMID:12190447
NASA Astrophysics Data System (ADS)
Wang, Xiao-Tian
2010-02-01
This paper deals with the problem of discrete time option pricing using the multifractional Black-Scholes model with transaction costs. Using a mean self-financing delta hedging argument in a discrete time setting, a European call option pricing formula is obtained. The minimal price of an option under transaction costs is obtained. In addition, we show that scaling and long range dependence have a significant impact on option pricing.
Pricing of European options under BS-BHM-updated model and its properties
NASA Astrophysics Data System (ADS)
Mutijah, Guritno, Suryo; Gunardi
2016-02-01
A European call option price formula under the BS-BHM-Updated model is studied in this paper. BS-BHM- Updated model is a BS-BHM model improved in applying Gaussian integral. The formula of European call and put options price is given in this paper too. Greeks and a good property of put-call parity for the formula of European call option price are found. In this paper are also given the numerical results of European call option price and the put-call parity relationship. Numerical results of European call option price under BS-BHM-Updated model, Black Scholes model, and BS-BHM model are presented.
Numerical solution for option pricing with stochastic volatility model
NASA Astrophysics Data System (ADS)
Mariani, Andi; Nugrahani, Endar H.; Lesmana, Donny C.
2016-01-01
The option pricing equations derived from stochatic volatility models in finance are often cast in the form of nonlinear partial differential equations. To solve the equations, we used the upwind finite difference scheme for the spatial discretisation and a fully implicit time-stepping scheme. The result of this scheme is a matrix system in the form of an M-Matrix and we proof that the approximate solution converges to the viscosity solution to the equation by showing that the scheme is monotone, consistent and stable. Numerical experiments are implemented to show that the behavior and the order of convergence of upwind finite difference method.
Pricing European option under the time-changed mixed Brownian-fractional Brownian model
NASA Astrophysics Data System (ADS)
Guo, Zhidong; Yuan, Hongjun
2014-07-01
This paper deals with the problem of discrete time option pricing by a mixed Brownian-fractional subdiffusive Black-Scholes model. Under the assumption that the price of the underlying stock follows a time-changed mixed Brownian-fractional Brownian motion, we derive a pricing formula for the European call option in a discrete time setting.
NASA Astrophysics Data System (ADS)
McCauley, J. L.; Gunaratne, G. H.; Bassler, K. E.
2007-07-01
We show that our earlier generalization of the Black-Scholes partial differential equation (pde) for variable diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, the equivalence of Black-Scholes to a Martingale was proven for the case of the Gaussian returns model by Harrison and Kreps, but we prove it for a much larger class of returns models where the returns diffusion coefficient depends irreducibly on both returns x and time t. That option prices blow up if fat tails in logarithmic returns x are included in market return is also proven.
A path-independent method for barrier option pricing in hidden Markov models
NASA Astrophysics Data System (ADS)
Rashidi Ranjbar, Hedieh; Seifi, Abbas
2015-12-01
This paper presents a method for barrier option pricing under a Black-Scholes model with Markov switching. We extend the option pricing method of Buffington and Elliott to price continuously monitored barrier options under a Black-Scholes model with regime switching. We use a regime switching random Esscher transform in order to determine an equivalent martingale pricing measure, and then solve the resulting multidimensional integral for pricing barrier options. We have calculated prices for down-and-out call options under a two-state hidden Markov model using two different Monte-Carlo simulation approaches and the proposed method. A comparison of the results shows that our method is faster than Monte-Carlo simulation methods.
NASA Astrophysics Data System (ADS)
Wang, Xiao-Tian
2010-02-01
This paper deals with the problem of discrete time option pricing by the fractional Black-Scholes model with transaction costs. By a mean self-financing delta-hedging argument in a discrete time setting, a European call option pricing formula is obtained. The minimal price C(t,St) of an option under transaction costs is obtained as timestep δt=((, which can be used as the actual price of an option. In fact, C(t,St) is an adjustment to the volatility in the Black-Scholes formula by using the modified volatility σ√{2}(( to replace the volatility σ, where {k}/{σ}<(, H>{1}/{2} is the Hurst exponent, and k is a proportional transaction cost parameter. In addition, we also show that timestep and long-range dependence have a significant impact on option pricing.
A Non-Gaussian Stock Price Model: Options, Credit and a Multi-Timescale Memory
NASA Astrophysics Data System (ADS)
Borland, L.
We review a recently proposed model of stock prices, based on astatistical feedback model that results in a non-Gaussian distribution of price changes. Applications to option pricing and the pricing of debt is discussed. A generalization to account for feedback effects over multiple timescales is also presented. This model reproduces most of the stylized facts (ie statistical anomalies) observed in real financial markets.
NASA Astrophysics Data System (ADS)
Lai, Yongzeng; Zeng, Yan; Xi, Xiaojing
2011-11-01
In this paper, we discuss control variate methods for Asian option pricing under exponential jump diffusion model for the underlying asset prices. Numerical results show that the new control variate XNCV is much more efficient than the classical control variate XCCV when used in pricing Asian options. For example, the variance reduction ratios by XCCV are no more than 120 whereas those by XNCV vary from 15797 to 49171 on average over sample sizes 1024, 2048, 4096, 8192, 16384 and 32768.
Pricing American put option on zero-coupon bond in a jump-extended CIR model
NASA Astrophysics Data System (ADS)
Deng, Guohe
2015-05-01
This paper presents a jump extension to the CIR model of the short interest rate with exponential distribution jumps. We derive an approximated price of an American put option on a defaultable-free, zero-coupon bond using the two-GJ approach based on combining an European put option and a Bermudan option with two possible exercise dates. Closed-form solutions for both the European put option and the Bermudan option are obtained by using multivariate Fourier transforms and characteristic functions. The accuracy and efficiency of the approximation are examined using the least-square Monte Carlo simulation as the benchmarks. Finally several numerical examples illustrating the results have been presented and the prices have been compared to the corresponding prices for American option in the pure diffusion model.
Pricing foreign equity option with stochastic volatility
NASA Astrophysics Data System (ADS)
Sun, Qi; Xu, Weidong
2015-11-01
In this paper we propose a general foreign equity option pricing framework that unifies the vast foreign equity option pricing literature and incorporates the stochastic volatility into foreign equity option pricing. Under our framework, the time-changed Lévy processes are used to model the underlying assets price of foreign equity option and the closed form pricing formula is obtained through the use of characteristic function methodology. Numerical tests indicate that stochastic volatility has a dramatic effect on the foreign equity option prices.
Option pricing for stochastic volatility model with infinite activity Lévy jumps
NASA Astrophysics Data System (ADS)
Gong, Xiaoli; Zhuang, Xintian
2016-08-01
The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.
On the Black-Scholes European Option Pricing Model Robustness and Generality
NASA Astrophysics Data System (ADS)
Takada, Hellinton Hatsuo; de Oliveira Siqueira, José
2008-11-01
The common presentation of the widely known and accepted Black-Scholes European option pricing model explicitly imposes some restrictions such as the geometric Brownian motion assumption for the underlying stock price. In this paper, these usual restrictions are relaxed using maximum entropy principle of information theory, Pearson's distribution system, market frictionless and risk-neutrality theories to the calculation of a unique risk-neutral probability measure calibrated with market parameters.
Option pricing: Stock price, stock velocity and the acceleration Lagrangian
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.; Du, Xin; Bhanap, Jitendra
2014-12-01
The industry standard Black-Scholes option pricing formula is based on the current value of the underlying security and other fixed parameters of the model. The Black-Scholes formula, with a fixed volatility, cannot match the market's option price; instead, it has come to be used as a formula for generating the option price, once the so called implied volatility of the option is provided as additional input. The implied volatility not only is an entire surface, depending on the strike price and maturity of the option, but also depends on calendar time, changing from day to day. The point of view adopted in this paper is that the instantaneous rate of return of the security carries part of the information that is provided by implied volatility, and with a few (time-independent) parameters required for a complete pricing formula. An option pricing formula is developed that is based on knowing the value of both the current price and rate of return of the underlying security which in physics is called velocity. Using an acceleration Lagrangian model based on the formalism of quantum mathematics, we derive the pricing formula for European call options. The implied volatility of the market can be generated by our pricing formula. Our option price is applied to foreign exchange rates and equities and the accuracy is compared with Black-Scholes pricing formula and with the market price.
A note on Black-Scholes pricing model for theoretical values of stock options
NASA Astrophysics Data System (ADS)
Edeki, S. O.; Ugbebor, O. O.; Owoloko, E. A.
2016-02-01
In this paper, we consider some conditions that transform the classical Black-Scholes Model for stock options valuation from its partial differential equation (PDE) form to an equivalent ordinary differential equation (ODE) form. In addition, we propose a relatively new semi-analytical method for the solution of the transformed Black-Scholes model. The obtained solutions via this method can be used to find the theoretical values of the stock options in relation to their fair prices. In considering the reliability and efficiency of the models, we test some cases and the results are in good agreement with the exact solution.
NASA Astrophysics Data System (ADS)
Lemmens, D.; Wouters, M.; Tempere, J.; Foulon, S.
2008-07-01
We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our analytical formulas are tested with numerical Monte Carlo simulations.
Pricing bounds for discrete arithmetic Asian options under Lévy models
NASA Astrophysics Data System (ADS)
Lemmens, D.; Liang, L. Z. J.; Tempere, J.; De Schepper, A.
2010-11-01
Analytical bounds for Asian options are almost exclusively available in the Black-Scholes framework. In this paper we derive bounds for the price of a discretely monitored arithmetic Asian option when the underlying asset follows an arbitrary Lévy process. Explicit formulas are given for Kou’s model, Merton’s model, the normal inverse Gaussian model, the CGMY model and the variance gamma model. The results are compared with the comonotonic upper bound, existing numerical results, Monte carlo simulations and in the case of the variance gamma model with an existing lower bound. The method outlined here provides lower and upper bounds that are quick to evaluate, and more accurate than existing bounds.
Numerically pricing American options under the generalized mixed fractional Brownian motion model
NASA Astrophysics Data System (ADS)
Chen, Wenting; Yan, Bowen; Lian, Guanghua; Zhang, Ying
2016-06-01
In this paper, we introduce a robust numerical method, based on the upwind scheme, for the pricing of American puts under the generalized mixed fractional Brownian motion (GMFBM) model. By using portfolio analysis and applying the Wick-Itô formula, a partial differential equation (PDE) governing the prices of vanilla options under the GMFBM is successfully derived for the first time. Based on this, we formulate the pricing of American puts under the current model as a linear complementarity problem (LCP). Unlike the classical Black-Scholes (B-S) model or the generalized B-S model discussed in Cen and Le (2011), the newly obtained LCP under the GMFBM model is difficult to be solved accurately because of the numerical instability which results from the degeneration of the governing PDE as time approaches zero. To overcome this difficulty, a numerical approach based on the upwind scheme is adopted. It is shown that the coefficient matrix of the current method is an M-matrix, which ensures its stability in the maximum-norm sense. Remarkably, we have managed to provide a sharp theoretic error estimate for the current method, which is further verified numerically. The results of various numerical experiments also suggest that this new approach is quite accurate, and can be easily extended to price other types of financial derivatives with an American-style exercise feature under the GMFBM model.
Supersymmetry in option pricing
NASA Astrophysics Data System (ADS)
Jana, T. K.; Roy, P.
2011-06-01
We use supersymmetry to find the isospectral partners of Black-Scholes Hamiltonian without a potential and with a double knock out barrier potential. The pricing kernels for these Hamiltonians have also been obtained.
Option pricing for non-Gaussian price fluctuations
NASA Astrophysics Data System (ADS)
Kleinert, Hagen
2004-07-01
From the path integral description of price fluctuations with non-Gaussian distributions we derive a stochastic calculus which replaces Itô's calculus for harmonic fluctuations. We set up a natural martingale for option pricing from the wealth balance of options, stocks, and bonds, and evaluate the resulting formula for truncated Lévy distributions. After this, an alternative formula is derived for a model of multivariant Gaussian price fluctuations which leads to non-Gaussian return distributions fitting Dow Jones data excellently from long to short time scales with a tail behavior e - x/ x3/2.
Path integral pricing of Wasabi option in the Black-Scholes model
NASA Astrophysics Data System (ADS)
Cassagnes, Aurelien; Chen, Yu; Ohashi, Hirotada
2014-11-01
In this paper, using path integral techniques, we derive a formula for a propagator arising in the study of occupation time derivatives. Using this result we derive a fair price for the case of the cumulative Parisian option. After confirming the validity of the derived result using Monte Carlo simulation, a new type of heavily path dependent derivative product is investigated. We derive an approximation for our so-called Wasabi option fair price and check the accuracy of our result with a Monte Carlo simulation.
NASA Astrophysics Data System (ADS)
Wang, Xiao-Tian
2011-05-01
This paper deals with the problem of discrete time option pricing using the fractional Black-Scholes model with transaction costs. Through the ‘anchoring and adjustment’ argument in a discrete time setting, a European call option pricing formula is obtained. The minimal price of an option under transaction costs is obtained. In addition, the relation between scaling and implied volatility smiles is discussed.
Louis Bachelier: The Father of Modern Option Pricing Theory.
ERIC Educational Resources Information Center
Sullivan, Edward J.; Weithers, Timothy M.
1991-01-01
Observes that, before 1973, determining a valuation formula for option prices was an elusive goal of financial economics. Discusses Louis Bachelier's early twentieth-century work on the problem. Notes that Bachelier derived a normal distribution for stock price movements by modeling price changes in specific way. Reviews Bachelier's option pricing…
Valuating Privacy with Option Pricing Theory
NASA Astrophysics Data System (ADS)
Berthold, Stefan; Böhme, Rainer
One of the key challenges in the information society is responsible handling of personal data. An often-cited reason why people fail to make rational decisions regarding their own informational privacy is the high uncertainty about future consequences of information disclosures today. This chapter builds an analogy to financial options and draws on principles of option pricing to account for this uncertainty in the valuation of privacy. For this purpose, the development of a data subject's personal attributes over time and the development of the attribute distribution in the population are modeled as two stochastic processes, which fit into the Binomial Option Pricing Model (BOPM). Possible applications of such valuation methods to guide decision support in future privacy-enhancing technologies (PETs) are sketched.
Renewal equations for option pricing
NASA Astrophysics Data System (ADS)
Montero, M.
2008-09-01
In this paper we will develop a methodology for obtaining pricing expressions for financial instruments whose underlying asset can be described through a simple continuous-time random walk (CTRW) market model. Our approach is very natural to the issue because it is based in the use of renewal equations, and therefore it enhances the potential use of CTRW techniques in finance. We solve these equations for typical contract specifications, in a particular but exemplifying case. We also show how a formal general solution can be found for more exotic derivatives, and we compare prices for alternative models of the underlying. Finally, we recover the celebrated results for the Wiener process under certain limits.
Partial derivative approach for option pricing in a simple stochastic volatility model
NASA Astrophysics Data System (ADS)
Montero, M.
2004-11-01
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model has already been introduced in the literature. We present a new approach to the problem, based on partial differential equations, which gives a different perspective to the issue. Within our framework we can easily consider several forms for the market price of volatility risk, and interpret their financial meaning. We thus recover solutions previously mentioned in the literature as well as obtaining new ones.
Pricing currency options in the mixed fractional Brownian motion
NASA Astrophysics Data System (ADS)
Sun, Lin
2013-08-01
This paper deals with the problem of pricing European currency options in the mixed fractional Brownian environment. Both the pricing formula and the mixed fractional partial differential equation for European call currency options are obtained. Some Greeks and the estimator of volatility are also provided. Empirical studies and simulation results confirm the theoretical findings and show that the mixed fractional Brownian pricing model is a reasonable one.
Pricing and hedging Asian basket spread options
NASA Astrophysics Data System (ADS)
Deelstra, Griselda; Petkovic, Alexandre; Vanmaele, Michèle
2010-04-01
Asian options, basket options and spread options have been extensively studied in the literature. However, few papers deal with the problem of pricing general Asian basket spread options. This paper aims to fill this gap. In order to obtain prices and Greeks in a short computation time, we develop approximation formulae based on comonotonicity theory and moment matching methods. We compare their relative performances and explain how to choose the best approximation technique as a function of the Asian basket spread characteristics. We also give explicitly the Greeks for our proposed methods. In the last section we extend our results to options denominated in foreign currency.
Option pricing during post-crash relaxation times
NASA Astrophysics Data System (ADS)
Dibeh, Ghassan; Harmanani, Haidar M.
2007-07-01
This paper presents a model for option pricing in markets that experience financial crashes. The stochastic differential equation (SDE) of stock price dynamics is coupled to a post-crash market index. The resultant SDE is shown to have stock price and time dependent volatility. The partial differential equation (PDE) for call prices is derived using risk-neutral pricing. European call prices are then estimated using Monte Carlo and finite difference methods. Results of the model show that call option prices after the crash are systematically less than those predicted by the Black-Scholes model. This is a result of the effect of non-constant volatility of the model that causes a volatility skew.
A Model-Free No-arbitrage Price Bound for Variance Options
Bonnans, J. Frederic; Tan Xiaolu
2013-08-01
We suggest a numerical approximation for an optimization problem, motivated by its applications in finance to find the model-free no-arbitrage bound of variance options given the marginal distributions of the underlying asset. A first approximation restricts the computation to a bounded domain. Then we propose a gradient projection algorithm together with the finite difference scheme to solve the optimization problem. We prove the general convergence, and derive some convergence rate estimates. Finally, we give some numerical examples to test the efficiency of the algorithm.
Dynamic option pricing with endogenous stochastic arbitrage
NASA Astrophysics Data System (ADS)
Contreras, Mauricio; Montalva, Rodrigo; Pellicer, Rely; Villena, Marcelo
2010-09-01
Only few efforts have been made in order to relax one of the key assumptions of the Black-Scholes model: the no-arbitrage assumption. This is despite the fact that arbitrage processes usually exist in the real world, even though they tend to be short-lived. The purpose of this paper is to develop an option pricing model with endogenous stochastic arbitrage, capable of modelling in a general fashion any future and underlying asset that deviate itself from its market equilibrium. Thus, this investigation calibrates empirically the arbitrage on the futures on the S&P 500 index using transaction data from September 1997 to June 2009, from here a specific type of arbitrage called “arbitrage bubble”, based on a t-step function, is identified and hence used in our model. The theoretical results obtained for Binary and European call options, for this kind of arbitrage, show that an investment strategy that takes advantage of the identified arbitrage possibility can be defined, whenever it is possible to anticipate in relative terms the amplitude and timespan of the process. Finally, the new trajectory of the stock price is analytically estimated for a specific case of arbitrage and some numerical illustrations are developed. We find that the consequences of a finite and small endogenous arbitrage not only change the trajectory of the asset price during the period when it started, but also after the arbitrage bubble has already gone. In this context, our model will allow us to calibrate the B-S model to that new trajectory even when the arbitrage already started.
Pricing convertible bonds based on a multi-stage compound-option model
NASA Astrophysics Data System (ADS)
Gong, Pu; He, Zhiwei; Zhu, Song-Ping
2006-07-01
In this paper, we introduce the concept of multi-stage compound options to the valuation of convertible bonds (CBs). Rather than evaluating a nested high-dimensional integral that has arisen from the valuation of multi-stage compound options, we found that adopting the finite difference method (FDM) to solve the Black-Scholes equation for each stage actually resulted in a better numerical efficiency. By comparing our results with those obtained by solving the Black-Scholes equation directly, we can show that the new approach does provide an approximation approach for the valuation of CBs and demonstrate that it offers a great potential for a further extension to CBs with more complex structures such as those with call and/or put provisions.
Stock price dynamics and option valuations under volatility feedback effect
NASA Astrophysics Data System (ADS)
Kanniainen, Juho; Piché, Robert
2013-02-01
According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price-dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations under the volatility feedback effect by modeling the joint dynamics of stock price, dividends, and volatility in continuous time. Most importantly, our model predicts the negative effect of an increase in squared return volatility on the value of deep-in-the-money call options and, furthermore, attempts to explain the volatility puzzle. We theoretically demonstrate a mechanism by which the market price of diffusion return risk, or an equity risk-premium, affects option prices and empirically illustrate how to identify that mechanism using forward-looking information on option contracts. Our theoretical and empirical results support the relevance of the volatility feedback effect. Overall, the results indicate that the prevailing practice of ignoring the time-varying dividend yield in option pricing can lead to oversimplification of the stock market dynamics.
Correlated continuous time random walk and option pricing
NASA Astrophysics Data System (ADS)
Lv, Longjin; Xiao, Jianbin; Fan, Liangzhong; Ren, Fuyao
2016-04-01
In this paper, we study a correlated continuous time random walk (CCTRW) with averaged waiting time, whose probability density function (PDF) is proved to follow stretched Gaussian distribution. Then, we apply this process into option pricing problem. Supposing the price of the underlying is driven by this CCTRW, we find this model captures the subdiffusive characteristic of financial markets. By using the mean self-financing hedging strategy, we obtain the closed-form pricing formulas for a European option with and without transaction costs, respectively. At last, comparing the obtained model with the classical Black-Scholes model, we find the price obtained in this paper is higher than that obtained from the Black-Scholes model. A empirical analysis is also introduced to confirm the obtained results can fit the real data well.
An Operator Splitting Method for Pricing American Options
NASA Astrophysics Data System (ADS)
Ikonen, Samuli; Toivanen, Jari
Pricing American options using partial (integro-)differential equation based methods leads to linear complementarity problems (LCPs). The numerical solution of these problems resulting from the Black-Scholes model, Kou's jump-diffusion model, and Heston's stochastic volatility model are considered. The finite difference discretization is described. The solutions of the discrete LCPs are approximated using an operator splitting method which separates the linear problem and the early exercise constraint to two fractional steps. The numerical experiments demonstrate that the prices of options can be computed in a few milliseconds on a PC.
On theoretical pricing of options with fuzzy estimators
NASA Astrophysics Data System (ADS)
Chrysafis, Konstantinos A.; Papadopoulos, Basil K.
2009-01-01
In this paper we present an application of a new method of constructing fuzzy estimators for the parameters of a given probability distribution function, using statistical data. This application belongs to the financial field and especially to the section of financial engineering. In financial markets there are great fluctuations, thus the element of vagueness and uncertainty is frequent. This application concerns Theoretical Pricing of Options and in particular the Black and Scholes Options Pricing formula. We make use of fuzzy estimators for the volatility of stock returns and we consider the stock price as a symmetric triangular fuzzy number. Furthermore we apply the Black and Scholes formula by using adaptive fuzzy numbers introduced by Thiagarajah et al. [K. Thiagarajah, S.S. Appadoo, A. Thavaneswaran, Option valuation model with adaptive fuzzy numbers, Computers and Mathematics with Applications 53 (2007) 831-841] for the stock price and the volatility and we replace the fuzzy volatility and the fuzzy stock price by possibilistic mean value. We refer to both cases of call and put option prices according to the Black & Scholes model and also analyze the results to Greek parameters. Finally, a numerical example is presented for both methods and a comparison is realized based on the results.
Testing option pricing with the Edgeworth expansion
NASA Astrophysics Data System (ADS)
Balieiro Filho, Ruy Gabriel; Rosenfeld, Rogerio
2004-12-01
There is a well-developed framework, the Black-Scholes theory, for the pricing of contracts based on the future prices of certain assets, called options. This theory assumes that the probability distribution of the returns of the underlying asset is a Gaussian distribution. However, it is observed in the market that this hypothesis is flawed, leading to the introduction of a fudge factor, the so-called volatility smile. Therefore, it would be interesting to explore extensions of the Black-Scholes theory to non-Gaussian distributions. In this paper, we provide an explicit formula for the price of an option when the distributions of the returns of the underlying asset is parametrized by an Edgeworth expansion, which allows for the introduction of higher independent moments of the probability distribution, namely skewness and kurtosis. We test our formula with options in the Brazilian and American markets, showing that the volatility smile can be reduced. We also check whether our approach leads to more efficient hedging strategies of these instruments.
Time-changed geometric fractional Brownian motion and option pricing with transaction costs
NASA Astrophysics Data System (ADS)
Gu, Hui; Liang, Jin-Rong; Zhang, Yun-Xiu
2012-08-01
This paper deals with the problem of discrete time option pricing by a fractional subdiffusive Black-Scholes model. The price of the underlying stock follows a time-changed geometric fractional Brownian motion. By a mean self-financing delta-hedging argument, the pricing formula for the European call option in discrete time setting is obtained.
A quantum model of option pricing: When Black-Scholes meets Schrödinger and its semi-classical limit
NASA Astrophysics Data System (ADS)
Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo; Ruiz, Aaron
2010-12-01
The Black-Scholes equation can be interpreted from the point of view of quantum mechanics, as the imaginary time Schrödinger equation of a free particle. When deviations of this state of equilibrium are considered, as a product of some market imperfection, such as: Transaction cost, asymmetric information issues, short-term volatility, extreme discontinuities, or serial correlations; the classical non-arbitrage assumption of the Black-Scholes model is violated, implying a non-risk-free portfolio. From Haven (2002) [1] we know that an arbitrage environment is a necessary condition to embedding the Black-Scholes option pricing model in a more general quantum physics setting. The aim of this paper is to propose a new Black-Scholes-Schrödinger model based on the endogenous arbitrage option pricing formulation introduced by Contreras et al. (2010) [2]. Hence, we derive a more general quantum model of option pricing, that incorporates arbitrage as an external time dependent force, which has an associated potential related to the random dynamic of the underlying asset price. This new resultant model can be interpreted as a Schrödinger equation in imaginary time for a particle of mass 1/σ2 with a wave function in an external field force generated by the arbitrage potential. As pointed out above, this new model can be seen as a more general formulation, where the perfect market equilibrium state postulated by the Black-Scholes model represent a particular case. Finally, since the Schrödinger equation is in place, we can apply semiclassical methods, of common use in theoretical physics, to find an approximate analytical solution of the Black-Scholes equation in the presence of market imperfections, as it is the case of an arbitrage bubble. Here, as a numerical illustration of the potential of this Schrödinger equation analogy, the semiclassical approximation is performed for different arbitrage bubble forms (step, linear and parabolic) and compare with the exact
Lie-algebraic approach for pricing moving barrier options with time-dependent parameters
NASA Astrophysics Data System (ADS)
Lo, C. F.; Hui, C. H.
2006-11-01
In this paper we apply the Lie-algebraic technique for the valuation of moving barrier options with time-dependent parameters. The value of the underlying asset is assumed to follow the constant elasticity of variance (CEV) process. By exploiting the dynamical symmetry of the pricing partial differential equations, the new approach enables us to derive the analytical kernels of the pricing formulae straightforwardly, and thus provides an efficient way for computing the prices of the moving barrier options. The method is also able to provide tight upper and lower bounds for the exact prices of CEV barrier options with fixed barriers. In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, our new approach could facilitate more efficient comparative pricing and precise risk management in equity derivatives with barriers by incorporating term-structures of interest rates, volatility and dividend into the CEV option valuation model.
El Farouq, Naïma; Bernhard, Pierre
2015-10-15
We prove the missing uniqueness theorem for the viscosity solution of a quasi-variational inequality related to a minimax impulse control problem modeling the option pricing with proportional transactions costs. This result makes our robust control approach of option pricing in the interval market model essentially complete.
Option Pricing with Log-stable Lévy Processes
NASA Astrophysics Data System (ADS)
Repetowicz, Przemysław; Richmond, Peter
We model the logarithm of the price (log-price) of a financial asset as a random variable obtained by projecting an operator stable random vector with a scaling index matrix \\underline{\\underline E} onto a non-random vector. The scaling index \\underline{\\underline E} models prices of the individual financial assets (stocks, mutual funds, etc.). We find the functional form of the characteristic function of real powers of the price returns and we compute the expectation value of these real powers and we speculate on the utility of these results for statistical inference. Finally we consider a portfolio composed of an asset and an option on that asset. We derive the characteristic function of the deviation of the portfolio, mathfrak{D}_t^{(mathfrak{t})} , defined as a temporal change of the portfolio diminished by the the compound interest earned. We derive pseudo-differential equations for the option as a function of the log-stock-price and time and we find exact closed-form solutions to that equation. These results were not known before. Finally we discuss how our solutions correspond to other approximate results known from literature,in particular to the well known Black & Scholes equation.
Risk-neutral density extraction from option prices: improved pricing with mixture density networks.
Schittenkopf, C; Dorffner, G
2001-01-01
One of the central goals in finance is to find better models for pricing and hedging financial derivatives such as call and put options. We present a new semi-nonparametric approach to risk-neutral density extraction from option prices, which is based on an extension of the concept of mixture density networks. The central idea is to model the shape of the risk-neutral density in a flexible, nonlinear way as a function of the time horizon. Thereby, stylized facts such as negative skewness and excess kurtosis are captured. The approach is applied to a very large set of intraday options data on the FTSE 100 recorded at LIFFE. It is shown to yield significantly better results in terms of out-of-sample pricing accuracy in comparison to the basic and an extended Black-Scholes model. It is also significantly better than a more elaborate GARCH option pricing model which includes a time-dependent volatility process. From the perspective of risk management, the extracted risk-neutral densities provide valuable information for value-at-risk estimations. PMID:18249907
On Asian option pricing for NIG Levy processes
NASA Astrophysics Data System (ADS)
Albrecher, Hansjorg; Predota, Martin
2004-11-01
In this paper, we derive approximations and bounds for the Esscher price of European-style arithmetic and geometric average options. The asset price process is assumed to be of exponential Levy type with normal inverse Gaussian (NIG) distributed log-returns. Numerical illustrations of the accuracy of these bounds as well as approximations and comparisons of the NIG average option prices with the corresponding Black-Scholes prices are given.
Pricing Asian options using moment matching on a multinomial lattice
NASA Astrophysics Data System (ADS)
Ogutu, Carolyne; Lundengârd, Karl; Silvestrov, Sergei; Weke, Patrick
2014-12-01
Pricing Asian options is often done using bi- or trinomial lattice methods. Here some results for generalizing these methods to lattices with more nodes are presented. We consider Asian option pricing on a lattice where the underlying asset follows Merton-Bates jump-diffusion model and describe the construction of a lattice using the moment matching technique which results in an equation system described by a rectangular Vandermonde matrix. The system is solved using the explicit expression for the inverse of the Vandermonde matrix and some restrictions on the jump sizes of the lattice and the distribution of moments are identified. The consequences of these restrictions for the suitability of the multinomial lattice methods are also discussed.
A homotopy analysis method for the option pricing PDE in illiquid markets
NASA Astrophysics Data System (ADS)
E-Khatib, Youssef
2012-09-01
One of the shortcomings of the Black and Scholes model on option pricing is the assumption that trading the underlying asset does not affect the underlying asset price. This can happen in perfectly liquid markets and it is evidently not viable in markets with imperfect liquidity (illiquid markets). It is well-known that markets with imperfect liquidity are more realistic. Thus, the presence of price impact while studying options is very important. This paper investigates a solution for the option pricing PDE in illiquid markets using the homotopy analysis method.
NASA Astrophysics Data System (ADS)
Zhang, Sumei; Wang, Lihe
2013-07-01
This study proposes a pricing model through allowing for stochastic interest rate and stochastic volatility in the double exponential jump-diffusion setting. The characteristic function of the proposed model is then derived. Fast numerical solutions for European call and put options pricing based on characteristic function and fast Fourier transform (FFT) technique are developed. Simulations show that our numerical technique is accurate, fast and easy to implement, the proposed model is suitable for modeling long-time real-market changes. The model and the proposed option pricing method are useful for empirical analysis of asset returns and risk management in firms.
Price of coupon bond options in a quantum field theory of forward interest rates
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
2006-10-01
European options on coupon bonds are studied in a quantum field theory model of forward interest rates. A approximation scheme for finding the option price is developed based on the fact that the volatility of the forward interest rate is a small quantity. The field theory for the forward interest rates is in effect Gaussian, and when the payoff function for the coupon bonds option is included it makes the field theory exponentially nonlinear. A Feynman perturbation expansion gives a result for the price of Libor swaption that agrees quite well with the market price.
NASA Astrophysics Data System (ADS)
Zhang, Xubo
This paper uses the approaches and models of option theory to analyze two-stage venture capital investment in agricultural production and processing enterprises decision-making under uncertainty. Mathematics expressions of this two-stage venture capital investment decision-making are presented. An option value model about two-stage venture capital investment decision-making base on options pricing theory under the uncertainty is presented. Get the solution of option pricing model which we present.
Pricing geometric Asian power options under mixed fractional Brownian motion environment
NASA Astrophysics Data System (ADS)
Prakasa Rao, B. L. S.
2016-03-01
It has been observed that the stock price process can be modeled with driving force as a mixed fractional Brownian motion with Hurst index H > 3/4 whenever long-range dependence is possibly present. We obtain a closed form expression for the price of a geometric Asian option under the mixed fractional Brownian motion environment. We consider also Asian power options when the payoff function is a power function.
Spectral method for pricing options in illiquid markets
NASA Astrophysics Data System (ADS)
Pindza, Edson; Patidar, Kailash C.
2012-09-01
We present a robust numerical method to solve a problem of pricing options in illiquid markets. The governing equation is described by a nonlinear Black-Scholes partial differential equation (BS-PDE) of the reaction-diffusion-advection type. To discretise this BS-PDE numerically, we use a spectral method in the asset (spatial) direction and couple it with a fifth order RADAU method for the discretisation in the time direction. Numerical experiments illustrate that our approach is very efficient for pricing financial options in illiquid markets.
Using Priced Options to Solve the Exposure Problem in Sequential Auctions
NASA Astrophysics Data System (ADS)
Mous, Lonneke; Robu, Valentin; La Poutré, Han
This paper studies the benefits of using priced options for solving the exposure problem that bidders with valuation synergies face when participating in multiple, sequential auctions. We consider a model in which complementary-valued items are auctioned sequentially by different sellers, who have the choice of either selling their good directly or through a priced option, after fixing its exercise price. We analyze this model from a decision-theoretic perspective and we show, for a setting where the competition is formed by local bidders, that using options can increase the expected profit for both buyers and sellers. Furthermore, we derive the equations that provide minimum and maximum bounds between which a synergy buyer's bids should fall in order for both sides to have an incentive to use the options mechanism. Next, we perform an experimental analysis of a market in which multiple synergy bidders are active simultaneously.
Pricing of swing options: A Monte Carlo simulation approach
NASA Astrophysics Data System (ADS)
Leow, Kai-Siong
We study the problem of pricing swing options, a class of multiple early exercise options that are traded in energy market, particularly in the electricity and natural gas markets. These contracts permit the option holder to periodically exercise the right to trade a variable amount of energy with a counterparty, subject to local volumetric constraints. In addition, the total amount of energy traded from settlement to expiration with the counterparty is restricted by a global volumetric constraint. Violation of this global volumetric constraint is allowed but would lead to penalty settled at expiration. The pricing problem is formulated as a stochastic optimal control problem in discrete time and state space. We present a stochastic dynamic programming algorithm which is based on piecewise linear concave approximation of value functions. This algorithm yields the value of the swing option under the assumption that the optimal exercise policy is applied by the option holder. We present a proof of an almost sure convergence that the algorithm generates the optimal exercise strategy as the number of iterations approaches to infinity. Finally, we provide a numerical example for pricing a natural gas swing call option.
Oscillatory Reduction in Option Pricing Formula Using Shifted Poisson and Linear Approximation
NASA Astrophysics Data System (ADS)
Nur Rachmawati, Ro'fah; Irene; Budiharto, Widodo
2014-03-01
Option is one of derivative instruments that can help investors improve their expected return and minimize the risks. However, the Black-Scholes formula is generally used in determining the price of the option does not involve skewness factor and it is difficult to apply in computing process because it produces oscillation for the skewness values close to zero. In this paper, we construct option pricing formula that involve skewness by modified Black-Scholes formula using Shifted Poisson model and transformed it into the form of a Linear Approximation in the complete market to reduce the oscillation. The results are Linear Approximation formula can predict the price of an option with very accurate and successfully reduce the oscillations in the calculation processes.
NASA Astrophysics Data System (ADS)
Kanai, Yasuhiro; Abe, Keiji; Seki, Yoichi
2015-06-01
We propose a price percolation model to reproduce the price distribution of components used in industrial finished goods. The intent is to show, using the price percolation model and a component category as an example, that percolation behaviors, which exist in the matter system, the ecosystem, and human society, also exist in abstract, random phenomena satisfying the power law. First, we discretize the total potential demand for a component category, considering it a random field. Second, we assume that the discretized potential demand corresponding to a function of a finished good turns into actual demand if the difficulty of function realization is less than the maximum difficulty of the realization. The simulations using this model suggest that changes in a component category's price distribution are due to changes in the total potential demand corresponding to the lattice size and the maximum difficulty of realization, which is an occupation probability. The results are verified using electronic components' sales data.
Federal Register 2010, 2011, 2012, 2013, 2014
2012-09-12
... From the Federal Register Online via the Government Publishing Office ] SECURITIES AND EXCHANGE COMMISSION Options Price Reporting Authority; Notice of Filing and Immediate Effectiveness of Proposed..., the Options Price Reporting Authority (``OPRA'') submitted to the Securities and Exchange...
Compact finite difference method for American option pricing
NASA Astrophysics Data System (ADS)
Zhao, Jichao; Davison, Matt; Corless, Robert M.
2007-09-01
A compact finite difference method is designed to obtain quick and accurate solutions to partial differential equation problems. The problem of pricing an American option can be cast as a partial differential equation. Using the compact finite difference method this problem can be recast as an ordinary differential equation initial value problem. The complicating factor for American options is the existence of an optimal exercise boundary which is jointly determined with the value of the option. In this article we develop three ways of combining compact finite difference methods for American option price on a single asset with methods for dealing with this optimal exercise boundary. Compact finite difference method one uses the implicit condition that solutions of the transformed partial differential equation be nonnegative to detect the optimal exercise value. This method is very fast and accurate even when the spatial step size h is large (h[greater-or-equal, slanted]0.1). Compact difference method two must solve an algebraic nonlinear equation obtained by Pantazopoulos (1998) at every time step. This method can obtain second order accuracy for space x and requires a moderate amount of time comparable with that required by the Crank Nicolson projected successive over relaxation method. Compact finite difference method three refines the free boundary value by a method developed by Barone-Adesi and Lugano [The saga of the American put, 2003], and this method can obtain high accuracy for space x. The last two of these three methods are convergent, moreover all the three methods work for both short term and long term options. Through comparison with existing popular methods by numerical experiments, our work shows that compact finite difference methods provide an exciting new tool for American option pricing.
An option pricing theory explanation of the invasion of Kuwait
Muhtaseb, M.R.
1995-12-31
The objective of this paper is to explain the invasion of Kuwait by making an analogy between a call option and the Iraq-Kuwait situation before the invasion on August 2, 1990. A number of factors contributed to the issuance of a deep-in-the money European call option to Iraq against Kuwait. The underlying asset is the crude oil reserves under Kuwait. Price of crude oil is determined in world spot markets. The exercise price is equal to the cost of permanently annexing and retaining Kuwait. The volatility is measured by the annualized variance of the weekly rate of return of the spot price of crude oil. Time-to-expiration is equal to the time period between decision date and actual invasion date. Finally, since crude oil prices are quoted in U.S. dollars, the U.S. Treasury bill rate is assumed to be the risk-free rate. In a base-case scenario, Kuwait`s oil reserves amount to 94,500 million barrels valued at $18 a barrell in early February 1990 resulting in a market value of $1,701 billion. Because the cost of the war to Iraq is not known, we assume it is comparable to that of the U.S.-led coalition of $51.0 billion. Time-to-expiration is six months. The treasury bill rate in early 1990 was around 7.5 percent. Annualized standard deviation of weekly rates of return is 0.216. The value of Kuwait`s invasion option is $1,642.25 billion. Depending on the scenario, the value of this special option ranged between $1,450 billion and $3.624 billion. 10 refs., 1 tab.
Federal Register 2010, 2011, 2012, 2013, 2014
2010-01-22
... COMMISSION Options Price Reporting Authority; Notice of Filing and Immediate Effectiveness of Proposed... December 28, 2009, the Options Price Reporting Authority (``OPRA'') submitted to the Securities and... will be members. The restructured OPRA will be known as Options Price Reporting Authority, LLC...
Perturbation expansion for option pricing with stochastic volatility
NASA Astrophysics Data System (ADS)
Jizba, Petr; Kleinert, Hagen; Haener, Patrick
2009-09-01
We fit the volatility fluctuations of the S&P 500 index well by a Chi distribution, and the distribution of log-returns by a corresponding superposition of Gaussian distributions. The Fourier transform of this is, remarkably, of the Tsallis type. An option pricing formula is derived from the same superposition of Black-Scholes expressions. An explicit analytic formula is deduced from a perturbation expansion around a Black-Scholes formula with the mean volatility. The expansion has two parts. The first takes into account the non-Gaussian character of the stock-fluctuations and is organized by powers of the excess kurtosis, the second is contract based, and is organized by the moments of moneyness of the option. With this expansion we show that for the Dow Jones Euro Stoxx 50 option data, a Δ-hedging strategy is close to being optimal.
Path integral pricing of outside barrier Asian options
NASA Astrophysics Data System (ADS)
Cassagnes, Aurelien; Chen, Yu; Ohashi, Hirotada
2014-01-01
Using the path-integral framework to cast the pricing problem of the outside barrier Asian option into a Wiener functional integral form, we show that, after the introduction of a law-equivalent process and transformation of the new system, the deviation from the Monte Carlo price is seen to be widely reduced. Bypassing the path-partitioning step, we show that our results behave nicely with respect to increasing correlation. After putting forward empirical evidence of this improvement, we extend the scope to a double knock-out outside barrier, and derive there an original formula. In the latter setting, we propose a simple scheme to reduce the relative error due to a nearby knock-out barrier.
Some Divergence Properties of Asset Price Models
NASA Astrophysics Data System (ADS)
Stummer, Wolfgang
2001-12-01
We consider asset price processes Xt which are weak solutions of one-dimensional stochastic differential equations of the form (equation (2)) Such price models can be interpreted as non-lognormally-distributed generalizations of the geometric Brownian motion. We study properties of the Iα-divergence between the law of the solution Xt and the corresponding drift-less measure (the special case α=1 is the relative entropy). This will be applied to some context in statistical information theory as well as to arbitrage theory and contingent claim valuation. For instance, the seminal option pricing theorems of Black-Scholes and Merton appear as a special case.
Pricing American Asian options with higher moments in the underlying distribution
NASA Astrophysics Data System (ADS)
Lo, Keng-Hsin; Wang, Kehluh; Hsu, Ming-Feng
2009-01-01
We develop a modified Edgeworth binomial model with higher moment consideration for pricing American Asian options. With lognormal underlying distribution for benchmark comparison, our algorithm is as precise as that of Chalasani et al. [P. Chalasani, S. Jha, F. Egriboyun, A. Varikooty, A refined binomial lattice for pricing American Asian options, Rev. Derivatives Res. 3 (1) (1999) 85-105] if the number of the time steps increases. If the underlying distribution displays negative skewness and leptokurtosis as often observed for stock index returns, our estimates can work better than those in Chalasani et al. [P. Chalasani, S. Jha, F. Egriboyun, A. Varikooty, A refined binomial lattice for pricing American Asian options, Rev. Derivatives Res. 3 (1) (1999) 85-105] and are very similar to the benchmarks in Hull and White [J. Hull, A. White, Efficient procedures for valuing European and American path-dependent options, J. Derivatives 1 (Fall) (1993) 21-31]. The numerical analysis shows that our modified Edgeworth binomial model can value American Asian options with greater accuracy and speed given higher moments in their underlying distribution.
Pricing of American style options with an adjoint process correction method
NASA Astrophysics Data System (ADS)
Jaekel, Uwe
2005-07-01
Pricing of American options is a more complicated problem than pricing of European options. In this work a formula is derived that allows the computation of the early exercise premium, i.e. the price difference between these two option types in terms of an adjoint process evolving in the reversed time direction of the original process determining the evolution of the European price. We show how this equation can be utilised to improve option price estimates from numerical schemes like finite difference or Monte Carlo methods.
Multi-layer model of correlated energy prices
NASA Astrophysics Data System (ADS)
Grine, Slimane; Diko, Pavel
2010-03-01
In this article we develop an extension of the affine jump-diffusion modeling framework and use it to build an intuitive and tractable model of an energy price complex. The development is motivated by the need to model prices of electricity while capturing their dependence on the price of other energy commodities. Such a model is essential for valuing a range of typical derivatives traded in the electricity markets: cross-commodity spread options, cross-location spread options, fuel-switching powerplants, etc. We give an approximate pricing method for these derivatives together with precise error bound estimates.
Option pricing beyond Black-Scholes based on double-fractional diffusion
NASA Astrophysics Data System (ADS)
Kleinert, H.; Korbel, J.
2016-05-01
We show how the prices of options can be determined with the help of double-fractional differential equation in such a way that their inclusion in a portfolio of stocks provides a more reliable hedge against dramatic price drops than the use of options whose prices were fixed by the Black-Scholes formula.
Black-Scholes option pricing within Itô and Stratonovich conventions
NASA Astrophysics Data System (ADS)
Perelló, J.; Porrà, J. M.; Montero, M.; Masoliver, J.
2000-04-01
Options are financial instruments designed to protect investors from the stock market randomness. In 1973, Black, Scholes and Merton proposed a very popular option pricing method using stochastic differential equations within the Itô interpretation. Herein, we derive the Black-Scholes equation for the option price using the Stratonovich calculus along with a comprehensive review, aimed to physicists, of the classical option pricing method based on the Itô calculus. We show, as can be expected, that the Black-Scholes equation is independent of the interpretation chosen. We nonetheless point out the many subtleties underlying Black-Scholes option pricing method.
Bounds for the price of discrete arithmetic Asian options
NASA Astrophysics Data System (ADS)
Vanmaele, M.; Deelstra, G.; Liinev, J.; Dhaene, J.; Goovaerts, M. J.
2006-01-01
In this paper the pricing of European-style discrete arithmetic Asian options with fixed and floating strike is studied by deriving analytical lower and upper bounds. In our approach we use a general technique for deriving upper (and lower) bounds for stop-loss premiums of sums of dependent random variables, as explained in Kaas et al. (Ins. Math. Econom. 27 (2000) 151-168), and additionally, the ideas of Rogers and Shi (J. Appl. Probab. 32 (1995) 1077-1088) and of Nielsen and Sandmann (J. Financial Quant. Anal. 38(2) (2003) 449-473). We are able to create a unifying framework for European-style discrete arithmetic Asian options through these bounds, that generalizes several approaches in the literature as well as improves the existing results. We obtain analytical and easily computable bounds. The aim of the paper is to formulate an advice of the appropriate choice of the bounds given the parameters, investigate the effect of different conditioning variables and compare their efficiency numerically. Several sets of numerical results are included. We also discuss hedging using these bounds. Moreover, our methods are applicable to a wide range of (pricing) problems involving a sum of dependent random variables.
Optional time-of-use prices for electricity: Analysis of PG E's experimental TOU rates
Train, K.; Mehrez, G.
1992-07-01
We examine customers' time-of-use (TOU) demand for electricity and their choice between standard and TOU rate schedules. We specify an econometric model in which the customer's demand curves determine the customer's choice of rate schedule. We estimate the model on data from Pacific Gas Electric Company's experiment with optional TOU prices in the residential sector. With the model, we compare the TOU consumption and price elasticities of customers who chose TOU rates with those who chose standard rates. We also estimate the impact of the TOU rates on the utility's revenues and costs. The analysis suggests that the TOU rates offered under PG E's experiment decreased PG E's profits and hence contributed to higher general rate levels. The model can be used, however, to design optional TOU rates that increase profits and lower general rate levels.
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.; Liang, Cui
2007-01-01
The quantum finance pricing formulas for coupon bond options and swaptions derived by Baaquie [Phys. Rev. E 75, 016703 (2006)] are reviewed. We empirically study the swaption market and propose an efficient computational procedure for analyzing the data. Empirical results of the swaption price, volatility, and swaption correlation are compared with the predictions of quantum finance. The quantum finance model generates the market swaption price to over 90% accuracy.
Modeling spot markets for electricity and pricing electricity derivatives
NASA Astrophysics Data System (ADS)
Ning, Yumei
Spot prices for electricity have been very volatile with dramatic price spikes occurring in restructured market. The task of forecasting electricity prices and managing price risk presents a new challenge for market players. The objectives of this dissertation are: (1) to develop a stochastic model of price behavior and predict price spikes; (2) to examine the effect of weather forecasts on forecasted prices; (3) to price electricity options and value generation capacity. The volatile behavior of prices can be represented by a stochastic regime-switching model. In the model, the means of the high-price and low-price regimes and the probabilities of switching from one regime to the other are specified as functions of daily peak load. The probability of switching to the high-price regime is positively related to load, but is still not high enough at the highest loads to predict price spikes accurately. An application of this model shows how the structure of the Pennsylvania-New Jersey-Maryland market changed when market-based offers were allowed, resulting in higher price spikes. An ARIMA model including temperature, seasonal, and weekly effects is estimated to forecast daily peak load. Forecasts of load under different assumptions about weather patterns are used to predict changes of price behavior given the regime-switching model of prices. Results show that the range of temperature forecasts from a normal summer to an extremely warm summer cause relatively small increases in temperature (+1.5%) and load (+3.0%). In contrast, the increases in prices are large (+20%). The conclusion is that the seasonal outlook forecasts provided by NOAA are potentially valuable for predicting prices in electricity markets. The traditional option models, based on Geometric Brownian Motion are not appropriate for electricity prices. An option model using the regime-switching framework is developed to value a European call option. The model includes volatility risk and allows changes
Kudryavtsev, Oleg
2013-01-01
In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is applicable for pricing barrier and American options. The pricing problem is reduced to the sequence of linear algebraic systems with a dense Toeplitz matrix; then the Wiener-Hopf factorization method is applied. We give an important probabilistic interpretation based on the infinitely divisible distributions theory to the Laurent operators in the correspondent factorization identity. Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix. However, our method is more accurate. We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments. PMID:24489518
2013-01-01
In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is applicable for pricing barrier and American options. The pricing problem is reduced to the sequence of linear algebraic systems with a dense Toeplitz matrix; then the Wiener-Hopf factorization method is applied. We give an important probabilistic interpretation based on the infinitely divisible distributions theory to the Laurent operators in the correspondent factorization identity. Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix. However, our method is more accurate. We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments. PMID:24489518
Model risk for European-style stock index options.
Gençay, Ramazan; Gibson, Rajna
2007-01-01
In empirical modeling, there have been two strands for pricing in the options literature, namely the parametric and nonparametric models. Often, the support for the nonparametric methods is based on a benchmark such as the Black-Scholes (BS) model with constant volatility. In this paper, we study the stochastic volatility (SV) and stochastic volatility random jump (SVJ) models as parametric benchmarks against feedforward neural network (FNN) models, a class of neural network models. Our choice for FNN models is due to their well-studied universal approximation properties of an unknown function and its partial derivatives. Since the partial derivatives of an option pricing formula are risk pricing tools, an accurate estimation of the unknown option pricing function is essential for pricing and hedging. Our findings indicate that FNN models offer themselves as robust option pricing tools, over their sophisticated parametric counterparts in predictive settings. There are two routes to explain the superiority of FNN models over the parametric models in forecast settings. These are nonnormality of return distributions and adaptive learning. PMID:17278472
Perpetual American vanilla option pricing under single regime change risk: an exhaustive study
NASA Astrophysics Data System (ADS)
Montero, Miquel
2009-07-01
Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in which some of the properties—volatility and dividend policy—of the underlying stock can change at a random instant of time but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because most relevant facts usually entail sharp predictable consequences. The effect of this potential risk on perpetual American vanilla options is remarkable: the very equation that will determine the fair price depends on the solution to be found. Sound results are found under the optics both of finance and physics. In particular, a parallelism among the overall outcome of this problem and a phase transition is established.
The Use of the Information Wave Function in a Drift Dependent Option Price: A Simple Example
Haven, Emmanuel
2009-03-10
This paper briefly describes how a drift-dependent option price is obtained, following the work of Tan. We briefly argue how the information wave function concept, which has now been used in various financial settings, can be used in this type of option price.
Variable step random walks, self-similar distributions, and pricing of options (Invited Paper)
NASA Astrophysics Data System (ADS)
Gunaratne, Gemunu H.; McCauley, Joseph L.
2005-05-01
A new theory for pricing of options is presented. It is based on the assumption that successive movements depend on the value of the return. The solution to the Fokker-Planck equation is shown to be an asymmetric exponential distribution, similar to those observed in intra-day currency markets. The "volatility smile", used by traders to correct the Black-Scholes pricing is shown to be a heuristic mechanism to implement options pricing formulae derived from our theory.
Pricing Models and Payment Schemes for Library Collections.
ERIC Educational Resources Information Center
Stern, David
2002-01-01
Discusses new pricing and payment options for libraries in light of online products. Topics include alternative cost models rather than traditional subscriptions; use-based pricing; changes in scholarly communication due to information technology; methods to determine appropriate charges for different organizations; consortial plans; funding; and…
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
2007-01-01
European options on coupon bonds are studied in a quantum field theory model of forward interest rates. Swaptions are briefly reviewed. An approximation scheme for the coupon bond option price is developed based on the fact that the volatility of the forward interest rates is a small quantity. The field theory for the forward interest rates is Gaussian, but when the payoff function for the coupon bond option is included it makes the field theory nonlocal and nonlinear. A perturbation expansion using Feynman diagrams gives a closed form approximation for the price of coupon bond option. A special case of the approximate bond option is shown to yield the industry standard one-factor HJM formula with exponential volatility.
NASA Astrophysics Data System (ADS)
Adamchuk, A. N.; Esipov, S. E.
1997-12-01
Methods of functional analysis are applied to describe collectively fluctuating default-free pure discount bonds subject to trading-related noise which generates arbitrage opportunities. Two key elements of the model are: (i) the naturally incorporated fixed bond price at maturity which is achieved by making use of only those fluctuating paths of price motion which terminate at a specified final condition, and (ii) the most attractive arbitrage opportunities between bonds with close maturities, with modeled a local linear approximation. The model can be written in different closed forms as a stochastic partial differential equation. The functional Black-Scholes equation for contingent claims is derived, and a connection with the conventional methods of option valuation is indicated.
Adaptive [theta]-methods for pricing American options
NASA Astrophysics Data System (ADS)
Khaliq, Abdul Q. M.; Voss, David A.; Kazmi, Kamran
2008-12-01
We develop adaptive [theta]-methods for solving the Black-Scholes PDE for American options. By adding a small, continuous term, the Black-Scholes PDE becomes an advection-diffusion-reaction equation on a fixed spatial domain. Standard implementation of [theta]-methods would require a Newton-type iterative procedure at each time step thereby increasing the computational complexity of the methods. Our linearly implicit approach avoids such complications. We establish a general framework under which [theta]-methods satisfy a discrete version of the positivity constraint characteristic of American options, and numerically demonstrate the sensitivity of the constraint. The positivity results are established for the single-asset and independent two-asset models. In addition, we have incorporated and analyzed an adaptive time-step control strategy to increase the computational efficiency. Numerical experiments are presented for one- and two-asset American options, using adaptive exponential splitting for two-asset problems. The approach is compared with an iterative solution of the two-asset problem in terms of computational efficiency.
Analysis of the discontinuous Galerkin method applied to the European option pricing problem
NASA Astrophysics Data System (ADS)
Hozman, J.
2013-12-01
In this paper we deal with a numerical solution of a one-dimensional Black-Scholes partial differential equation, an important scalar nonstationary linear convection-diffusion-reaction equation describing the pricing of European vanilla options. We present a derivation of the numerical scheme based on the space semidiscretization of the model problem by the discontinuous Galerkin method with nonsymmetric stabilization of diffusion terms and with the interior and boundary penalty. The main attention is paid to the investigation of a priori error estimates for the proposed scheme. The appended numerical experiments illustrate the theoretical results and the potency of the method, consequently.
Pricing American options for interest rate caps and coupon bonds in quantum finance
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.; Liang, Cui
2007-07-01
American option for interest rate caps and coupon bonds are analyzed in the formalism of quantum finance. Calendar time and future time are discretized to yield a lattice field theory of interest rates that provides an efficient numerical algorithm for evaluating the price of American options. The algorithm is shown to hold over a wide range of strike prices and coupon rates. All the theoretical constraints that American options have to obey are shown to hold for the numerical prices of American interest rate caps and coupon bond options. Non-trivial correlation between the different interest rates are efficiently incorporated in the numerical algorithm. New inequalities are conjectured, based on the results of the numerical study, for American options on interest rate instruments.
Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion
Sun, Jiao-Jiao; Zhou, Shengwu; Zhang, Yan; Han, Miao; Wang, Fei
2014-01-01
The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed. PMID:27433525
On smoothing of the Crank-Nicolson scheme and higher order schemes for pricing barrier options
NASA Astrophysics Data System (ADS)
Wade, B. A.; Khaliq, A. Q. M.; Yousuf, M.; Vigo-Aguiar, J.; Deininger, R.
2007-07-01
Most option pricing problems have nonsmooth payoffs or discontinuous derivatives at the exercise price. Discrete barrier options have not only nonsmooth payoffs but also time dependent discontinuities. In pricing barrier options, certain aspects are triggered if the asset price becomes too high or too low. Standard smoothing schemes used to solve problems with nonsmooth payoff do not work well for discrete barrier options because of discontinuities introduced in the time domain when each barrier is applied. Moreover, these unwanted oscillations become worse when estimating the hedging parameters, e.g., Delta and Gamma. We have an improved smoothing strategy for the Crank-Nicolson method which is unique in achieving optimal order convergence for barrier option problems. Numerical experiments are discussed for one asset and two asset problems. Time evolution graphs are obtained for one asset problems to show how option prices change with respect to time. This smoothing strategy is then extended to higher order methods using diagonal (m,m)--Pade main schemes under a smoothing strategy of using as damping schemes the (0,2m-1) subdiagonal Pade schemes.
Fast pricing of American options by linear programming
Dempster, M.; Hutton, J.P.
1994-12-31
This paper describes a new method for computation of the value of various American options on underlying dividend bearing securities under standard Black-Scholes assumptions. It is well known that the problem of valuing the American put can be expressed as solving an abstract linear complementarity problem in terms of a parabolic partial differential operator. Generalizing earlier work of Cryer, Dempster and Borwein for elliptic operators, we show that the American put option value function is the solution of an abstract linear programme bounded by the payoff at exercise. Different American options require only different payoff function bounds. Standard finite difference or finite element approximations to the complementarity problem lead to ordinary linear programmes. We report promising computational results for several American option types using IBM`s Optimization System Library on an RS6000/590.
Optional time-of-use prices for electricity: Analysis of PG&E`s experimental TOU rates. Final report
Train, K.; Mehrez, G.
1992-07-01
We examine customers` time-of-use (TOU) demand for electricity and their choice between standard and TOU rate schedules. We specify an econometric model in which the customer`s demand curves determine the customer`s choice of rate schedule. We estimate the model on data from Pacific Gas & Electric Company`s experiment with optional TOU prices in the residential sector. With the model, we compare the TOU consumption and price elasticities of customers who chose TOU rates with those who chose standard rates. We also estimate the impact of the TOU rates on the utility`s revenues and costs. The analysis suggests that the TOU rates offered under PG&E`s experiment decreased PG&E`s profits and hence contributed to higher general rate levels. The model can be used, however, to design optional TOU rates that increase profits and lower general rate levels.
Transmission pricing and renewables: Issues, options, and recommendations
Stoft, S.; Webber, C.; Wiser, R.
1997-05-01
Open access to the transmission system, if provided at reasonable costs, should open new electricity markets for high-quality renewable resources that are located far from load centers. Several factors will affect the cost of transmission service, including the type of transmission pricing system implemented and the specific attributes of renewable energy. One crucial variable in the transmission cost equation is a generator`s capacity factor. This factor is important for intermittent renewables such as wind and solar, because it can increase transmission costs several fold due to the traditional use of take-or-pay, capacity-based transmission access charges. This report argues that such a charge is demonstrably unfair to renewable generators. It puts them at an economic disadvantage that will lead to an undersupply of renewable energy compared with the least-cost mix of generation technologies. The authors argue that congestion charges must first be separated from the access charges that cover the fixed cost of the network before one can design an efficient tariff. They then show that, in a competitive market with a separate charge for congestion, a take-or-pay capacity-based access charge used to cover system fixed costs cannot be justified on the basis of peak-load pricing. An energy-based access charge, on the other hand, is fair to intermittent generators as well as to the usual spectrum of peak and base-load technologies. This report also reviews other specific characteristics of renewables that can affect the cost of transmission, and evaluates the potential impact on renewables of several transmission pricing schemes, including postage-stamp rates, megawatt-mile pricing, congestion pricing, and the Federal Energy Regulatory Commission`s {open_quotes}point-to-point{close_quotes} transmission tariffs.
The modified Black-Scholes model via constant elasticity of variance for stock options valuation
NASA Astrophysics Data System (ADS)
Edeki, S. O.; Owoloko, E. A.; Ugbebor, O. O.
2016-02-01
In this paper, the classical Black-Scholes option pricing model is visited. We present a modified version of the Black-Scholes model via the application of the constant elasticity of variance model (CEVM); in this case, the volatility of the stock price is shown to be a non-constant function unlike the assumption of the classical Black-Scholes model.
Nguyen, Tuan Anh; Knight, Rosemary; Roughead, Elizabeth Ellen; Brooks, Geoffrey; Mant, Andrea
2015-03-01
Pharmaceutical expenditure is rising globally. Most high-income countries have exercised pricing or purchasing strategies to address this pressure. Low- and middle-income countries (LMICs), however, usually have less regulated pharmaceutical markets and often lack feasible pricing or purchasing strategies, notwithstanding their wish to effectively manage medicine budgets. In high-income countries, most medicines payments are made by the state or health insurance institutions. In LMICs, most pharmaceutical expenditure is out-of-pocket which creates a different dynamic for policy enforcement. The paucity of rigorous studies on the effectiveness of pharmaceutical pricing and purchasing strategies makes it especially difficult for policy makers in LMICs to decide on a course of action. This article reviews published articles on pharmaceutical pricing and purchasing policies. Many policy options for medicine pricing and purchasing have been found to work but they also have attendant risks. No one option is decisively preferred; rather a mix of options may be required based on country-specific context. Empirical studies in LMICs are lacking. However, risks from any one policy option can reasonably be argued to be greater in LMICs which often lack strong legal systems, purchasing and state institutions to underpin the healthcare system. Key factors are identified to assist LMICs improve their medicine pricing and purchasing systems. PMID:24425694
Numerical pricing of options using high-order compact finite difference schemes
NASA Astrophysics Data System (ADS)
Tangman, D. Y.; Gopaul, A.; Bhuruth, M.
2008-09-01
We consider high-order compact (HOC) schemes for quasilinear parabolic partial differential equations to discretise the Black-Scholes PDE for the numerical pricing of European and American options. We show that for the heat equation with smooth initial conditions, the HOC schemes attain clear fourth-order convergence but fail if non-smooth payoff conditions are used. To restore the fourth-order convergence, we use a grid stretching that concentrates grid nodes at the strike price for European options. For an American option, an efficient procedure is also described to compute the option price, Greeks and the optimal exercise curve. Comparisons with a fourth-order non-compact scheme are also done. However, fourth-order convergence is not experienced with this strategy. To improve the convergence rate for American options, we discuss the use of a front-fixing transformation with the HOC scheme. We also show that the HOC scheme with grid stretching along the asset price dimension gives accurate numerical solutions for European options under stochastic volatility.
NASA Astrophysics Data System (ADS)
Klibanov, Michael V.; Kuzhuget, Andrey V.; Golubnichiy, Kirill V.
2016-01-01
A new empirical mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock, new initial and new boundary conditions. Conventional notions of maturity time and strike prices are not used. The Black-Scholes equation is solved as a parabolic equation with the reversed time, which is an ill-posed problem. Thus, a regularization method is used to solve it. To verify the validity of our model, real market data for 368 randomly selected liquid options are used. A new trading strategy is proposed. Our results indicates that our method is profitable on those options. Furthermore, it is shown that the performance of two simple extrapolation-based techniques is much worse. We conjecture that our method might lead to significant profits of those financial insitutions which trade large amounts of options. We caution, however, that further studies are necessary to verify this conjecture.
NASA Astrophysics Data System (ADS)
von Sydow, Lina
2013-10-01
The discontinuous Galerkin method for time integration of the Black-Scholes partial differential equation for option pricing problems is studied and compared with more standard time-integrators. In space an adaptive finite difference discretization is employed. The results show that the dG method are in most cases at least comparable to standard time-integrators and in some cases superior to them. Together with adaptive spatial grids the suggested pricing method shows great qualities.
Pricing European options with a log Student’s t-distribution: A Gosset formula
NASA Astrophysics Data System (ADS)
Cassidy, Daniel T.; Hamp, Michael J.; Ouyed, Rachid
2010-12-01
The distributions of returns for stocks are not well described by a normal probability density function (pdf). Student’s t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student’s t-distribution, which we call a Gosset approach in honour of W.S. Gosset, the author behind the nom de plume Student. The approach that we present can be used to price European options using other distributions and yields the Black-Scholes formula for returns described by a normal pdf.
Option pricing from wavelet-filtered financial series
NASA Astrophysics Data System (ADS)
de Almeida, V. T. X.; Moriconi, L.
2012-10-01
We perform wavelet decomposition of high frequency financial time series into large and small time scale components. Taking the FTSE100 index as a case study, and working with the Haar basis, it turns out that the small scale component defined by most (≃99.6%) of the wavelet coefficients can be neglected for the purpose of option premium evaluation. The relevance of the hugely compressed information provided by low-pass wavelet-filtering is related to the fact that the non-gaussian statistical structure of the original financial time series is essentially preserved for expiration times which are larger than just one trading day.
Multi-factor energy price models and exotic derivatives pricing
NASA Astrophysics Data System (ADS)
Hikspoors, Samuel
The high pace at which many of the world's energy markets have gradually been opened to competition have generated a significant amount of new financial activity. Both academicians and practitioners alike recently started to develop the tools of energy derivatives pricing/hedging as a quantitative topic of its own. The energy contract structures as well as their underlying asset properties set the energy risk management industry apart from its more standard equity and fixed income counterparts. This thesis naturally contributes to these broad market developments in participating to the advances of the mathematical tools aiming at a better theory of energy contingent claim pricing/hedging. We propose many realistic two-factor and three-factor models for spot and forward price processes that generalize some well known and standard modeling assumptions. We develop the associated pricing methodologies and propose stable calibration algorithms that motivate the application of the relevant modeling schemes.
A new perspective on Quantum Finance using the Black-Scholes pricing model
NASA Astrophysics Data System (ADS)
Dieng, Lamine
2007-03-01
Options are known to be divided into two types, the first type is called a call option and the second type is called a put option and these options are offered to stock holders in order to hedge their positions against risky fluctuations of the stock price. It is important to mention that due to fluctuations of the stock price, options can be found sometimes deep in the money, at the money and out of the money. A deep in the money option is described when the option's holder has a positive expected payoff, at the money option is when the option's holder has a zero expected payoff and an out of the money option is when the payoff is negative. In this work, we will assume the stock price to be described by the well known Black-Scholes model or sometimes called the multiplicative model. Using Ito calculus, Martingale and supermartingale theories, we investigated the Black-Scholes pricing equation at the money (X(stock price)= K (strike price)) when the expected payoff of the options holder is zero. We also hedged the Black-Scholes pricing equation in the limit when delta is zero to obtain the non-relativistic time independent Schroedinger equation in quantum mechanics. We compared the two equations and found the diffusion constant to be a function of the stock price in contrast to the Bachelier model we have worked on earlier. We solved the Schroedinger equation and found a dependence between interest rate, volatility and strike price at the money.
Federal Register 2010, 2011, 2012, 2013, 2014
2010-12-07
... not firm while showing the actual price and size of the firm side of the quote. This has proved to be... correctly reflect the actual state of the market. For this reason, OPRA is now proposing to add to Sections... considered for the purpose of determining what is the BBO in the subject option, but the firm side of...
The wave-equivalent of the Black-Scholes option price: an interpretation
NASA Astrophysics Data System (ADS)
Haven, Emmanuel
2004-12-01
We propose an interpretation of the wave-equivalent of the Black-Scholes option price. We consider Nelson's version of the Brownian motion (Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, NJ, 1967) and we use this specific motion as an input to produce a Black-Scholes PDE with a risk premium.
Federal Register 2010, 2011, 2012, 2013, 2014
2010-11-12
... From the Federal Register Online via the Government Publishing Office SECURITIES AND EXCHANGE COMMISSION Options Price Reporting Authority; Notice of Filing and Immediate Effectiveness of Proposed Amendment To Revise the Device-Based Professional Subscriber Fees Charged by OPRA for its Basic Service November 8, 2010. Pursuant to Section 11A...
48 CFR 1552.217-77 - Option to extend the term of the contract fixed price.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Option to extend the term of the contract fixed price. 1552.217-77 Section 1552.217-77 Federal Acquisition Regulations System ENVIRONMENTAL PROTECTION AGENCY CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT CLAUSES Texts...
On decoupling of volatility smile and term structure in inverse option pricing
NASA Astrophysics Data System (ADS)
Egger, Herbert; Hein, Torsten; Hofmann, Bernd
2006-08-01
Correct pricing of options and other financial derivatives is of great importance to financial markets and one of the key subjects of mathematical finance. Usually, parameters specifying the underlying stochastic model are not directly observable, but have to be determined indirectly from observable quantities. The identification of local volatility surfaces from market data of European vanilla options is one very important example of this type. As with many other parameter identification problems, the reconstruction of local volatility surfaces is ill-posed, and reasonable results can only be achieved via regularization methods. Moreover, due to the sparsity of data, the local volatility is not uniquely determined, but depends strongly on the kind of regularization norm used and a good a priori guess for the parameter. By assuming a multiplicative structure for the local volatility, which is motivated by the specific data situation, the inverse problem can be decomposed into two separate sub-problems. This removes part of the non-uniqueness and allows us to establish convergence and convergence rates under weak assumptions. Additionally, a numerical solution of the two sub-problems is much cheaper than that of the overall identification problem. The theoretical results are illustrated by numerical tests.
Options for pricing ancillary services in a deregulated power system
NASA Astrophysics Data System (ADS)
Yamin, Hatim Yahya
2001-07-01
GENCOs in restructured systems are compensated for selling energy in the market. In a restructured market, a mechanism is required to entice participants in the market to provide ancillary services and to ensure adequate compensation that would guarantee its economic viability. The ISO controls the dispatch of generation, manages the reliability of the transmission grid, provides open access to the transmission, buys and provides ancillary services as required, coordinates day-ahead, hour-ahead schedules and performs real time balancing of load and generation, settles real time imbalances and ancillary services sales and purchases. The ISO, also, administers congestion management protocols for the transmission grid. Since the ISO does not own any generating units it must ensure that there is enough reserves for maintaining reliability according to FERC regulations, and sufficient unloaded generating capacity for balancing services in a real-time market. The ISO could meet these requirements by creating a competitive market for ancillary services, which are metered and remain unbundled to provide an accurate compensation for each supplier and cost to each consumer, In this study, we give an overview for restructuring and ancillary services in a restructured power marketplace. Also, we discuss the effect of GENCOs' actions in the competitive energy and ancillary service markets. In addition, we propose an auction market design for hedging ancillary service costs in California market. Furthermore, we show how to include the n-1 and voltage contingencies in security constrained unit commitment. Finally, we present two approaches for GENCOs' unit commitment in a restructured power market; one is based on game theory and the other is based on market price forecasting. In each of the two GENCOs' unit commitment approaches, we discuss the GENCOs' optimal bidding strategies in energy and ancillary service markets to maximize the GENCOs' profit.
The Shuttle Cost and Price model
NASA Technical Reports Server (NTRS)
Leary, Katherine; Stone, Barbara
1983-01-01
The Shuttle Cost and Price (SCP) model was developed as a tool to assist in evaluating major aspects of Shuttle operations that have direct and indirect economic consequences. It incorporates the major aspects of NASA Pricing Policy and corresponds to the NASA definition of STS operating costs. An overview of the SCP model is presented and the cost model portion of SCP is described in detail. Selected recent applications of the SCP model to NASA Pricing Policy issues are presented.
Option pricing formulas and nonlinear filtering: a Feynman path integral perspective
NASA Astrophysics Data System (ADS)
Balaji, Bhashyam
2013-05-01
Many areas of engineering and applied science require the solution of certain parabolic partial differential equa tions, such as the Fokker-Planck and Kolmogorov equations. The fundamental solution, or the Green's function, for such PDEs can be written in terms of the Feynman path integral (FPI). The partial differential equation arising in the valuing of options is the Kolmogorov backward equation that is referred to as the Black-Scholes equation. The utility of this is demonstrated and numerical examples that illustrate the high accuracy of option price calculation even when using a fairly coarse grid.
Convergence analysis of a monotonic penalty method for American option pricing
NASA Astrophysics Data System (ADS)
Zhang, Kai; Yang, Xiaoqi; Teo, Kok Lay
2008-12-01
This paper is devoted to study the convergence analysis of a monotonic penalty method for pricing American options. A monotonic penalty method is first proposed to solve the complementarity problem arising from the valuation of American options, which produces a nonlinear degenerated parabolic PDE with Black-Scholes operator. Based on the variational theory, the solvability and convergence properties of this penalty approach are established in a proper infinite dimensional space. Moreover, the convergence rate of the combination of two power penalty functions is obtained.
NASA Astrophysics Data System (ADS)
Egger, Herbert; Engl, Heinz W.
2005-06-01
This paper investigates the stable identification of local volatility surfaces σ(S, t) in the Black-Scholes/Dupire equation from market prices of European Vanilla options. Based on the properties of the parameter-to-solution mapping, which assigns option prices to given volatilities, we show stability and convergence of approximations gained by Tikhonov regularization. In the case of a known term-structure of the volatility surface, in particular, if the volatility is assumed to be constant in time, we prove convergence rates under simple smoothness and decay conditions on the true volatility. The convergence rate analysis sheds light onto the importance of an appropriate a priori guess for the unknown volatility and the nature of the ill-posedness of the inverse problem, caused by smoothing properties and the nonlinearity of the direct problem. Finally, the theoretical results are illustrated by numerical experiments.
Multi-dimensional option pricing using radial basis functions and the generalized Fourier transform
NASA Astrophysics Data System (ADS)
Larsson, Elisabeth; Ahlander, Krister; Hall, Andreas
2008-12-01
We show that the generalized Fourier transform can be used for reducing the computational cost and memory requirements of radial basis function methods for multi-dimensional option pricing. We derive a general algorithm, including a transformation of the Black-Scholes equation into the heat equation, that can be used in any number of dimensions. Numerical experiments in two and three dimensions show that the gain is substantial even for small problem sizes. Furthermore, the gain increases with the number of dimensions.
Code of Federal Regulations, 2010 CFR
2010-10-01
... and Service Contract Act-Price Adjustment (Multiple Year and Option Contracts). 52.222-43 Section 52... Standards Act and Service Contract Act—Price Adjustment (Multiple Year and Option Contracts). As prescribed...—Price Adjustment (Multiple Year and Option Contracts) (SEP 2009) (a) This clause applies to...
Essays on pricing dynamics, price dispersion, and nested logit modelling
NASA Astrophysics Data System (ADS)
Verlinda, Jeremy Alan
The body of this dissertation comprises three standalone essays, presented in three respective chapters. Chapter One explores the possibility that local market power contributes to the asymmetric relationship observed between wholesale costs and retail prices in gasoline markets. I exploit an original data set of weekly gas station prices in Southern California from September 2002 to May 2003, and take advantage of highly detailed station and local market-level characteristics to determine the extent to which spatial differentiation influences price-response asymmetry. I find that brand identity, proximity to rival stations, bundling and advertising, operation type, and local market features and demographics each influence a station's predicted asymmetric relationship between prices and wholesale costs. Chapter Two extends the existing literature on the effect of market structure on price dispersion in airline fares by modeling the effect at the disaggregate ticket level. Whereas past studies rely on aggregate measures of price dispersion such as the Gini coefficient or the standard deviation of fares, this paper estimates the entire empirical distribution of airline fares and documents how the shape of the distribution is determined by market structure. Specifically, I find that monopoly markets favor a wider distribution of fares with more mass in the tails while duopoly and competitive markets exhibit a tighter fare distribution. These findings indicate that the dispersion of airline fares may result from the efforts of airlines to practice second-degree price discrimination. Chapter Three adopts a Bayesian approach to the problem of tree structure specification in nested logit modelling, which requires a heavy computational burden in calculating marginal likelihoods. I compare two different techniques for estimating marginal likelihoods: (1) the Laplace approximation, and (2) reversible jump MCMC. I apply the techniques to both a simulated and a travel mode
An inverse problem of determining the implied volatility in option pricing
NASA Astrophysics Data System (ADS)
Deng, Zui-Cha; Yu, Jian-Ning; Yang, Liu
2008-04-01
In the Black-Scholes world there is the important quantity of volatility which cannot be observed directly but has a major impact on the option value. In practice, traders usually work with what is known as implied volatility which is implied by option prices observed in the market. In this paper, we use an optimal control framework to discuss an inverse problem of determining the implied volatility when the average option premium, namely the average value of option premium corresponding with a fixed strike price and all possible maturities from the current time to a chosen future time, is known. The issue is converted into a terminal control problem by Green function method. The existence and uniqueness of the minimum of the control functional are addressed by the optimal control method, and the necessary condition which must be satisfied by the minimum is also given. The results obtained in the paper may be useful for those who engage in risk management or volatility trading.
Quantum model for the price dynamics
NASA Astrophysics Data System (ADS)
Choustova, Olga
2008-10-01
We apply methods of quantum mechanics to mathematical modelling of price dynamics in a financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Our model is a quantum-like model of the financial market, cf. with works of W. Segal, I.E. Segal, E. Haven. In this paper we study the problem of smoothness of price-trajectories in the Bohmian financial model. We show that even the smooth evolution of the financial pilot wave [psi](t,x) (representing expectations of traders) can induce jumps of prices of shares.
NASA Astrophysics Data System (ADS)
Liang, L. Z. J.; Lemmens, D.; Tempere, J.
2010-06-01
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations.
Pricing Models Using Real Data
ERIC Educational Resources Information Center
Obremski, Tom
2008-01-01
A practical hands-on classroom exercise is described and illustrated using the price of an item as dependent variable throughout. The exercise is well-tested and affords the instructor a variety of approaches and levels.
National Models for College Costs and Prices.
ERIC Educational Resources Information Center
Cunningham, Alisa F.; Merisotis, Jamie P.
2002-01-01
Examined the relationships among college prices, expenditures, and revenues within the public and private not-for-profit sectors. The trend analysis and model results found differences in the nature and strength of relationships between costs and prices across types of institutions and within types of institutions over time. (EV)
Convergence of the binomial tree method for Asian options in jump-diffusion models
NASA Astrophysics Data System (ADS)
Kim, Kwang Ik; Qian, Xiao-Song
2007-06-01
The binomial tree methods (BTM), first proposed by Cox, Ross and Rubinstein [J. Cox, S. Ross, M. Rubinstein, Option pricing: A simplified approach, J. Finan. Econ. 7 (1979) 229-264] in diffusion models and extended by Amin [K.I. Amin, Jump diffusion option valuation in discrete time, J. Finance 48 (1993) 1833-1863] to jump-diffusion models, is one of the most popular approaches to pricing options. In this paper, we present a binomial tree method for Asian options in jump-diffusion models and show its equivalence to certain explicit difference scheme. Employing numerical analysis and the notion of viscosity solution, we prove the uniform convergence of the binomial tree method for European-style and American-style Asian options.
Modeling asset price processes based on mean-field framework
NASA Astrophysics Data System (ADS)
Ieda, Masashi; Shiino, Masatoshi
2011-12-01
We propose a model of the dynamics of financial assets based on the mean-field framework. This framework allows us to construct a model which includes the interaction among the financial assets reflecting the market structure. Our study is on the cutting edge in the sense of a microscopic approach to modeling the financial market. To demonstrate the effectiveness of our model concretely, we provide a case study, which is the pricing problem of the European call option with short-time memory noise.
Improved radial basis function methods for multi-dimensional option pricing
NASA Astrophysics Data System (ADS)
Pettersson, Ulrika; Larsson, Elisabeth; Marcusson, Gunnar; Persson, Jonas
2008-12-01
In this paper, we have derived a radial basis function (RBF) based method for the pricing of financial contracts by solving the Black-Scholes partial differential equation. As an example of a financial contract that can be priced with this method we have chosen the multi-dimensional European basket call option. We have shown numerically that our scheme is second-order accurate in time and spectrally accurate in space for constant shape parameter. For other non-optimal choices of shape parameter values, the resulting convergence rate is algebraic. We propose an adapted node point placement that improves the accuracy compared with a uniform distribution. Compared with an adaptive finite difference method, the RBF method is 20-40 times faster in one and two space dimensions and has approximately the same memory requirements.
a Merton-Like Approach to Pricing Debt Based on a Non-Gaussian Asset Model
NASA Astrophysics Data System (ADS)
Borland, Lisa; Evnine, Jeremy; Pochart, Benoit
2005-09-01
We propose a generalization to Merton's model for evaluating credit spreads. In his original work, a company's assets were assumed to follow a log-normal process. We introduce fat tails and skew into this model, along the same lines as in the option pricing model of Borland and Bouchaud (2004, Quantitative Finance 4) and illustrate the effects of each component. Preliminary empirical results indicate that this model fits well to empirically observed credit spreads with a parameterization that also matched observed stock return distributions and option prices.
NASA Astrophysics Data System (ADS)
Li, Xibao
Residential time-of-use (TOU) rates have been in practice in the U.S. since the 1970s. However, for institutional, political, and regulatory reasons, only a very small proportion of residential customers are actually on these schedules. In this thesis, I explore why this is the case by empirically investigating two groups of questions: (1) On the "supply" side: Do utilities choose to offer TOU rates in residential sectors on their own initiative if state commissions do not order them to do so? Since utilities have other options, what is the relationship between the TOU rate and other alternatives? To answer these questions, I survey residential tariffs offered by more than 100 major investor-owned utilities, study the impact of various factors on utilities' rate-making behavior, and examine utility revealed preferences among four rate options: seasonal rates, inverted block rates, demand charges, and TOU rates. Estimated results suggest that the scale of residential sectors and the revenue contribution from residential sectors are the only two significant factors that influence utility decisions on offering TOU rates. Technical and economic considerations are not significant statistically. This implies that the little acceptance of TOU rates is partly attributed to utilities' inadequate attention to TOU rate design. (2) On the "demand" side: For utilities offering TOU tariffs, why do only a very small proportion of residential customers choose these tariffs? What factors influence customer choices? Unlike previous studies that used individual-level experimental data, this research employs actual aggregated information from 29 utilities offering optional TOU rates. By incorporating neo-classical demand analysis into an aggregated random coefficient logit model, I investigate the impact of both price and non-price tariff characteristics and non-tariff factors on customer choice behavior. The analysis indicates that customer pure tariff preference (which captures the
NASA Astrophysics Data System (ADS)
Bouchaud, Jean-Philippe; Sornette, Didier
1994-06-01
The ability to price risks and devise optimal investment strategies in thé présence of an uncertain "random" market is thé cornerstone of modern finance theory. We first consider thé simplest such problem of a so-called "European call option" initially solved by Black and Scholes using Ito stochastic calculus for markets modelled by a log-Brownien stochastic process. A simple and powerful formalism is presented which allows us to generalize thé analysis to a large class of stochastic processes, such as ARCH, jump or Lévy processes. We also address thé case of correlated Gaussian processes, which is shown to be a good description of three différent market indices (MATIF, CAC40, FTSE100). Our main result is thé introduction of thé concept of an optimal strategy in the sense of (functional) minimization of the risk with respect to the portfolio. If the risk may be made to vanish for particular continuous uncorrelated 'quasiGaussian' stochastic processes (including Black and Scholes model), this is no longer the case for more general stochastic processes. The value of the residual risk is obtained and suggests the concept of risk-corrected option prices. In the presence of very large deviations such as in Lévy processes, new criteria for rational fixing of the option prices are discussed. We also apply our method to other types of options, `Asian', `American', and discuss new possibilities (`doubledecker'...). The inclusion of transaction costs leads to the appearance of a natural characteristic trading time scale. L'aptitude à quantifier le coût du risque et à définir une stratégie optimale de gestion de portefeuille dans un marché aléatoire constitue la base de la théorie moderne de la finance. Nous considérons d'abord le problème le plus simple de ce type, à savoir celui de l'option d'achat `européenne', qui a été résolu par Black et Scholes à l'aide du calcul stochastique d'Ito appliqué aux marchés modélisés par un processus Log
Black-Scholes finite difference modeling in forecasting of call warrant prices in Bursa Malaysia
NASA Astrophysics Data System (ADS)
Mansor, Nur Jariah; Jaffar, Maheran Mohd
2014-07-01
Call warrant is a type of structured warrant in Bursa Malaysia. It gives the holder the right to buy the underlying share at a specified price within a limited period of time. The issuer of the structured warrants usually uses European style to exercise the call warrant on the maturity date. Warrant is very similar to an option. Usually, practitioners of the financial field use Black-Scholes model to value the option. The Black-Scholes equation is hard to solve analytically. Therefore the finite difference approach is applied to approximate the value of the call warrant prices. The central in time and central in space scheme is produced to approximate the value of the call warrant prices. It allows the warrant holder to forecast the value of the call warrant prices before the expiry date.
Electricity market pricing, risk hedging and modeling
NASA Astrophysics Data System (ADS)
Cheng, Xu
In this dissertation, we investigate the pricing, price risk hedging/arbitrage, and simplified system modeling for a centralized LMP-based electricity market. In an LMP-based market model, the full AC power flow model and the DC power flow model are most widely used to represent the transmission system. We investigate the differences of dispatching results, congestion pattern, and LMPs for the two power flow models. An appropriate LMP decomposition scheme to quantify the marginal costs of the congestion and real power losses is critical for the implementation of financial risk hedging markets. However, the traditional LMP decomposition heavily depends on the slack bus selection. In this dissertation we propose a slack-independent scheme to break LMP down into energy, congestion, and marginal loss components by analyzing the actual marginal cost of each bus at the optimal solution point. The physical and economic meanings of the marginal effect at each bus provide accurate price information for both congestion and losses, and thus the slack-dependency of the traditional scheme is eliminated. With electricity priced at the margin instead of the average value, the market operator typically collects more revenue from power sellers than that paid to power buyers. According to the LMP decomposition results, the revenue surplus is then divided into two parts: congestion charge surplus and marginal loss revenue surplus. We apply the LMP decomposition results to the financial tools, such as financial transmission right (FTR) and loss hedging right (LHR), which have been introduced to hedge against price risks associated to congestion and losses, to construct a full price risk hedging portfolio. The two-settlement market structure and the introduction of financial tools inevitably create market manipulation opportunities. We investigate several possible market manipulation behaviors by virtual bidding and propose a market monitor approach to identify and quantify such
Majority orienting model for the oscillation of market price
NASA Astrophysics Data System (ADS)
Takahashi, H.; Itoh, Y.
2004-01-01
The present paper introduces a majority orienting model in which the dealers' behavior changes based on the influence of the price to show the oscillation of stock price in the stock market. We show the oscillation of the price for the model by applying the vanderPol equation which is a deterministic approximation of our model.
Option trading and oil futures markets
Chassard, C.; Halliwell, M.
1986-01-01
This book describes mechanics of options trading, particularly their use to complement trading in oil futures and forward markets to increase agents' flexibility in hedging against price risks. The main determinants of option premiums and a number of option pricing models are discussed as are the Black and Scholes Model, issues of options and oil-indexed bonds: The Philbro Proposal, NYMEX Crude Oil Option Contract and Standard Oil Issue.
Food Prices and Climate Extremes: A Model of Global Grain Price Variability with Storage
NASA Astrophysics Data System (ADS)
Otto, C.; Schewe, J.; Frieler, K.
2015-12-01
Extreme climate events such as droughts, floods, or heat waves affect agricultural production in major cropping regions and therefore impact the world market prices of staple crops. In the last decade, crop prices exhibited two very prominent price peaks in 2007-2008 and 2010-2011, threatening food security especially for poorer countries that are net importers of grain. There is evidence that these spikes in grain prices were at least partly triggered by actual supply shortages and the expectation of bad harvests. However, the response of the market to supply shocks is nonlinear and depends on complex and interlinked processes such as warehousing, speculation, and trade policies. Quantifying the contributions of such different factors to short-term price variability remains difficult, not least because many existing models ignore the role of storage which becomes important on short timescales. This in turn impedes the assessment of future climate change impacts on food prices. Here, we present a simple model of annual world grain prices that integrates grain stocks into the supply and demand functions. This firstly allows us to model explicitly the effect of storage strategies on world market price, and thus, for the first time, to quantify the potential contribution of trade policies to price variability in a simple global framework. Driven only by reported production and by long--term demand trends of the past ca. 40 years, the model reproduces observed variations in both the global storage volume and price of wheat. We demonstrate how recent price peaks can be reproduced by accounting for documented changes in storage strategies and trade policies, contrasting and complementing previous explanations based on different mechanisms such as speculation. Secondly, we show how the integration of storage allows long-term projections of grain price variability under climate change, based on existing crop yield scenarios.
Modeling and simulation of consumer response to dynamic pricing.
Valenzuela, J.; Thimmapuram, P.; Kim, J
2012-08-01
Assessing the impacts of dynamic-pricing under the smart grid concept is becoming extremely important for deciding its full deployment. In this paper, we develop a model that represents the response of consumers to dynamic pricing. In the model, consumers use forecasted day-ahead prices to shift daily energy consumption from hours when the price is expected to be high to hours when the price is expected to be low while maintaining the total energy consumption as unchanged. We integrate the consumer response model into the Electricity Market Complex Adaptive System (EMCAS). EMCAS is an agent-based model that simulates restructured electricity markets. We explore the impacts of dynamic-pricing on price spikes, peak demand, consumer energy bills, power supplier profits, and congestion costs. A simulation of an 11-node test network that includes eight generation companies and five aggregated consumers is performed for a period of 1 month. In addition, we simulate the Korean power system.
Barbose, Galen; Goldman, Charles; Bharvirkar, Ranjit; Hopper,Nicole; Ting, Michael; Neenan, Bernie
2005-08-01
Demand response (DR) has been broadly recognized to be an integral component of well-functioning electricity markets, although currently underdeveloped in most regions. Among the various initiatives undertaken to remedy this deficiency, public utility commissions (PUC) and utilities have considered implementing dynamic pricing tariffs, such as real-time pricing (RTP), and other retail pricing mechanisms that communicate an incentive for electricity consumers to reduce their usage during periods of high generation supply costs or system reliability contingencies. Efforts to introduce DR into retail electricity markets confront a range of basic policy issues. First, a fundamental issue in any market context is how to organize the process for developing and implementing DR mechanisms in a manner that facilitates productive participation by affected stakeholder groups. Second, in regions with retail choice, policymakers and stakeholders face the threshold question of whether it is appropriate for utilities to offer a range of dynamic pricing tariffs and DR programs, or just ''plain vanilla'' default service. Although positions on this issue may be based primarily on principle, two empirical questions may have some bearing--namely, what level of price response can be expected through the competitive retail market, and whether establishing RTP as the default service is likely to result in an appreciable level of DR? Third, if utilities are to have a direct role in developing DR, what types of retail pricing mechanisms are most appropriate and likely to have the desired policy impact (e.g., RTP, other dynamic pricing options, DR programs, or some combination)? Given a decision to develop utility RTP tariffs, three basic implementation issues require attention. First, should it be a default or optional tariff, and for which customer classes? Second, what types of tariff design is most appropriate, given prevailing policy objectives, wholesale market structure, ratemaking
Creating New Pricing Models for Electronic Publishing.
ERIC Educational Resources Information Center
Boelio, David B.; Knight, Nancy H.
Establishing pricing policies for electronic publishing that are fair and flexible is of vital importance to the information industry. The pricing of most information available electronically is far less efficient and market-sensitive than it could be. Some of the new approaches to pricing, emphasizing a usage-based metric providing qualitative…
Spatial Data Web Services Pricing Model Infrastructure
NASA Astrophysics Data System (ADS)
Ozmus, L.; Erkek, B.; Colak, S.; Cankurt, I.; Bakıcı, S.
2013-08-01
most important law with related NSDI is the establishment of General Directorate of Geographic Information System under the Ministry of Environment and Urbanism. due to; to do or to have do works and activities with related to the establishment of National Geographic Information Systems (NGIS), usage of NGIS and improvements of NGIS. Outputs of these projects are served to not only public administration but also to Turkish society. Today for example, TAKBIS data (cadastre services) are shared more than 50 institutions by Web services, Tusaga-Aktif system has more than 3800 users who are having real-time GPS data correction, Orthophoto WMS services has been started for two years as a charge of free. Today there is great discussion about data pricing among the institutions. Some of them think that the pricing is storage of the data. Some of them think that the pricing is value of data itself. There is no certain rule about pricing. On this paper firstly, pricing of data storage and later on spatial data pricing models in different countries are investigated to improve institutional understanding in Turkey.
Pricing of pharmaceuticals. Assessing the pricing potential by a pricing matrix model.
Nuijten, Mark J C; Kosa, Joszef
2004-06-01
Pricing and reimbursement of new pharmaceuticals have been based until recently on the traditional clinical trial outcomes (efficacy, safety, and quality parameters) used for registration. Now we can distinguish various additional data requirements which relate to the use of the drug in real daily practice. The most important new data requirements are effectiveness, cost-effectiveness, and budgetary impact. A main question is how much the impact is of the various types of data in the pricing and reimbursement process. The objective of this contribution is to present a method for quantifying this type of uncertainty in order to develop a more solid pricing and reimbursement strategy for a new innovative drug. The concepts are illustrated for a new hypothetical antidepressant drug in The Netherlands. This method is based on the analytic hierarchy process (AHP) concept which measures decision makers' preferences for the critical success factors. This study shows that the AHP concept may be applied to the pricing and reimbursement environment. The method may be used to assess the pricing potential of a new drug, considering the various data requirements in the reimbursement process. PMID:15452745
Pricing equity warrants with a promised lowest price in Merton's jump-diffusion model
NASA Astrophysics Data System (ADS)
Xiao, Weilin; Zhang, Xili
2016-09-01
Motivated by the empirical evidence of jumps in the dynamics of firm behavior, this paper considers the problem of pricing equity warrants in the presence of a promised lowest price when the price of the underlying asset follows the Merton's jump-diffusion process. Using the Martingale approach, we propose a valuation model of equity warrants based on the firm value, its volatility, and parameters of the jump component, which are not directly observable. To implement our pricing model empirically, this paper also provides a promising estimation method for obtaining these desired variables based on observable data, such as stock prices and the book value of total liability. We conduct an empirical study to ascertain the performance of our proposed model using the data of Changdian warrant collected from 25 May 2006 (the listing date) to 29 January 2007 (the expiration date). Furthermore, the comparison of traditional models (such as the Black-Scholes model, the Noreen-Wolfson model, the Lauterbach-Schultz model, and the Ukhov model) with our model is presented. From the empirical study, we can see that the mean absolute error of our pricing model is 16.75%. By contrast, the Black-Scholes model, the Noreen-Wolfson model, the Lauterbach-Schultz model, and the Ukhov model applied to the same warrant produce mean absolute errors of 92.24%, 45.38%, 87.34%, 76.12%, respectively. Thus both the dilution effect and the jump feature cannot be ignored in determining the valuation of equity warrants.
Exploring Management Options for Increasing Corn Land on NY Farms Affected by Rising Corn Prices
Technology Transfer Automated Retrieval System (TEKTRAN)
New York dairy farms use their most fertile land to produce corn silage, an important component of their production system. Increasing demand for corn by ethanol producers is driving up corn grain prices. This is introducing a major shift into the NY dairy farm system by prompting farmers to place m...
Modeling the Impact of Energy and Water Prices on Reservoir and Aquifer Management
NASA Astrophysics Data System (ADS)
Dale, L. L.; Vicuna, S.; Faybishenko, B.
2008-12-01
Climate change and polices to limit carbon emissions are likely to increase energy and water scarcity and raise prices. These price impacts affect the way that reservoirs and aquifers should be managed to maximize the value of water and energy outputs. In this paper, we use a model of storage in a specific region to illustrate how energy and water prices affect optimal reservoir and aquifer management. We evaluate reservoir-aquifer water management in the Merced water basin in California, applying an optimization model of storage benefits associated with different management options and input prices. The model includes two submodels: (a) a monthly nonlinear submodel for optimization of the conjunctive energy/water use and (b) an inter-annual stochastic dynamic programming submodel used for determining an operating rule matrix which maximizes system benefits for given economic and hydrologic conditions. The model input parameters include annual inflows, initial storage, crop water demands, crop prices and electricity prices. The model is used to determine changes in net energy generation and water delivery and associated changes in water storage levels caused by changes in water and energy output prices. For the scenario of water/energy tradeoffs for a pure reservoir (with no groundwater use), we illustrate the tradeoff between the agricultural water use and hydropower generation (MWh) for different energy/agriculture price ratios. The analysis is divided into four steps. The first and second steps describe these price impacts on reservoirs and aquifers, respectively. The third step covers price impacts on conjunctive reservoir and aquifer management. The forth step describes price impacts on reservoir and aquifer storage in the more common historical situation, when these facilities are managed separately. The study indicates that optimal reservoir and aquifer storage levels are a positive function of the energy to water price ratio. The study also concludes that
A fast high-order finite difference algorithm for pricing American options
NASA Astrophysics Data System (ADS)
Tangman, D. Y.; Gopaul, A.; Bhuruth, M.
2008-12-01
We describe an improvement of Han and Wu's algorithm [H. Han, X.Wu, A fast numerical method for the Black-Scholes equation of American options, SIAM J. Numer. Anal. 41 (6) (2003) 2081-2095] for American options. A high-order optimal compact scheme is used to discretise the transformed Black-Scholes PDE under a singularity separating framework. A more accurate free boundary location based on the smooth pasting condition and the use of a non-uniform grid with a modified tridiagonal solver lead to an efficient implementation of the free boundary value problem. Extensive numerical experiments show that the new finite difference algorithm converges rapidly and numerical solutions with good accuracy are obtained. Comparisons with some recently proposed methods for the American options problem are carried out to show the advantage of our numerical method.
Petroleum property valuation: A binomial lattice implementation of option price theory
Pickles, E. ); Smith, J.L. )
1993-01-01
The authors take a simple tutorial approach to explain how option valuation can be applied in practice to the petroleum industry. They discuss a simple spreadsheet formulation, demonstrate how required input data can be extracted from market information, and give several exploration and development examples. Under the market and fiscal conditions described they derive the value of discovered, undeveloped reserves projected to result from offshore licensing in the United Kingdom, and they show how to determine the maximum amount that should be committed to an exploration work program to find those reserves. Lease-bidding and farm-out applications are briefly described. The authors recommend option valuation as an alternative to discounted cash flow analysis in situations where cash flows are uncertain and management has operating flexibility to adjust investment during the life of the project, and point to further work needed to fully value nested or embedded options. 10 refs., 9 figs.
Time series ARIMA models for daily price of palm oil
NASA Astrophysics Data System (ADS)
Ariff, Noratiqah Mohd; Zamhawari, Nor Hashimah; Bakar, Mohd Aftar Abu
2015-02-01
Palm oil is deemed as one of the most important commodity that forms the economic backbone of Malaysia. Modeling and forecasting the daily price of palm oil is of great interest for Malaysia's economic growth. In this study, time series ARIMA models are used to fit the daily price of palm oil. The Akaike Infromation Criterion (AIC), Akaike Infromation Criterion with a correction for finite sample sizes (AICc) and Bayesian Information Criterion (BIC) are used to compare between different ARIMA models being considered. It is found that ARIMA(1,2,1) model is suitable for daily price of crude palm oil in Malaysia for the year 2010 to 2012.
78 FR 10265 - Pricing for the 2013 Commemorative Coin Programs-Silver and Clad Coin Options
Federal Register 2010, 2011, 2012, 2013, 2014
2013-02-13
... announcing prices for the 2013 Girl Scouts of the USA Centennial Silver Dollar and the 2013 5-Star Generals... Centennial 50.95 55.95 Uncirculated Silver Dollar 2013 5-Star Generals Proof Silver Dollar 54.95 59.95 2013 5-Star Generals Uncirculated Silver 50.95 55.95 Dollar 2013 5-Star Generals Proof Half Dollar.. 17.95...
Fuzzy pricing for urban water resources: model construction and application.
Zhao, Ranhang; Chen, Shouyu
2008-08-01
A rational water price system plays a crucial role in the optimal allocation of water resources. In this paper, a fuzzy pricing model for urban water resources is presented, which consists of a multi-criteria fuzzy evaluation model and a water resources price (WRP) computation model. Various factors affecting WRP are comprehensively evaluated with multiple levels and objectives in the multi-criteria fuzzy evaluation model, while the price vectors of water resources are constructed in the WRP computation model according to the definition of the bearing water price index, and then WRP is calculated. With the incorporation of an operator's knowledge, it considers iterative weights and subjective preference of operators for weight-assessment. The weights determined are more rational and the evaluation results are more realistic. Particularly, dual water supply is considered in the study. Different prices being fixed for water resources with different qualities conforms to the law of water resources value (WRV) itself. A high-quality groundwater price computation model is also proposed to provide optimal water allocation and to meet higher living standards. The developed model is applied in Jinan for evaluating its validity. The method presented in this paper offers some new directions in the research of WRP. PMID:17499421
Convergence of the Approximation Scheme to American Option Pricing via the Discrete Morse Semiflow
Ishii, Katsuyuki; Omata, Seiro
2011-12-15
We consider the approximation scheme to the American call option via the discrete Morse semiflow, which is a minimizing scheme of a time semi-discretized variational functional. In this paper we obtain a rate of convergence of approximate solutions and the convergence of approximate free boundaries. We mainly apply the theory of variational inequalities and that of viscosity solutions to prove our results.
Analysis of a decision model in the context of equilibrium pricing and order book pricing
NASA Astrophysics Data System (ADS)
Wagner, D. C.; Schmitt, T. A.; Schäfer, R.; Guhr, T.; Wolf, D. E.
2014-12-01
An agent-based model for financial markets has to incorporate two aspects: decision making and price formation. We introduce a simple decision model and consider its implications in two different pricing schemes. First, we study its parameter dependence within a supply-demand balance setting. We find realistic behavior in a wide parameter range. Second, we embed our decision model in an order book setting. Here, we observe interesting features which are not present in the equilibrium pricing scheme. In particular, we find a nontrivial behavior of the order book volumes which reminds of a trend switching phenomenon. Thus, the decision making model alone does not realistically represent the trading and the stylized facts. The order book mechanism is crucial.
Feedback options in nonlinear numerical finance
NASA Astrophysics Data System (ADS)
Hugger, Jens; Mashayekhi, Sima
2012-09-01
Feedback options are options where information about the trading of the underlying asset is fed back into the pricing model. This results in nonlinear pricing models. A survey of the literature about feedback options in finance is presented. The pricing model for the full feedback option on an infinite slab is presented and boundary values on a bounded domain are derived. This bounded, nonlinear, 2 dimensional initial-boundary value problem is solved numerically using a number of standard finite difference schemes and the methods incorporated in the symbolic software Maple{trade mark, serif}.
Random trinomial tree models and vanilla options
NASA Astrophysics Data System (ADS)
Ganikhodjaev, Nasir; Bayram, Kamola
2013-09-01
In this paper we introduce and study random trinomial model. The usual trinomial model is prescribed by triple of numbers (u, d, m). We call the triple (u, d, m) an environment of the trinomial model. A triple (Un, Dn, Mn), where {Un}, {Dn} and {Mn} are the sequences of independent, identically distributed random variables with 0 < Dn < 1 < Un and Mn = 1 for all n, is called a random environment and trinomial tree model with random environment is called random trinomial model. The random trinomial model is considered to produce more accurate results than the random binomial model or usual trinomial model.
Brownian motion model with stochastic parameters for asset prices
NASA Astrophysics Data System (ADS)
Ching, Soo Huei; Hin, Pooi Ah
2013-09-01
The Brownian motion model may not be a completely realistic model for asset prices because in real asset prices the drift μ and volatility σ may change over time. Presently we consider a model in which the parameter x = (μ,σ) is such that its value x (t + Δt) at a short time Δt ahead of the present time t depends on the value of the asset price at time t + Δt as well as the present parameter value x(t) and m-1 other parameter values before time t via a conditional distribution. The Malaysian stock prices are used to compare the performance of the Brownian motion model with fixed parameter with that of the model with stochastic parameter.
Numerical Solution of a Model Equation of Price Formation
NASA Astrophysics Data System (ADS)
Chernogorova, T.; Vulkov, L.
2009-10-01
The paper [2] is devoted to the effect of reconciling the classical Black-Sholes theory of option pricing and hedging with various phenomena observed in the markets such as the influence of trading and hedging on the dynamics of an asset. Here we will discuss the numerical solution of initial boundary-value problems to a model equation of the theory. The lack of regularity in the solution as a result from Dirac delta coefficient reduces the accuracy in the numerical computations. First, we apply the finite volume method to discretize the differential problem. Second, we implement a technique of local regularization introduced by A-K. Tornberg and B. Engquist [7] for handling this equation. We derived the numerical regularization process into two steps: the Dirac delta function is regularized and then the regularized differential equation is discretized by difference schemes. Using the discrete maximum principle a priori bounds are obtained for the difference equations that imply stability and convergence of difference schemes for the problem under consideration. Numerical experiments are discussed.
Quantum modeling of nonlinear dynamics of stock prices: Bohmian approach
NASA Astrophysics Data System (ADS)
Choustova, O.
2007-08-01
We use quantum mechanical methods to model the price dynamics in the financial market mathematically. We propose describing behavioral financial factors using the pilot-wave (Bohmian) model of quantum mechanics. The real price trajectories are determined (via the financial analogue of the second Newton law) by two financial potentials: the classical-like potential V (q) (“hard” market conditions) and the quantumlike potential U(q) (behavioral market conditions).
Symmetry analysis of a model for the exercise of a barrier option
NASA Astrophysics Data System (ADS)
O'Hara, J. G.; Sophocleous, C.; Leach, P. G. L.
2013-09-01
A barrier option takes into account the possibility of an unacceptable change in the price of the underlying stock. Such a change could carry considerable financial loss. We examine one model based upon the Black-Scholes-Merton Equation and determine the functional forms of the barrier function and rebate function which are consistent with a solution of the underlying evolution partial differential equation using the Lie Theory of Extended Groups. The solution is consistent with the possibility of no rebate and the barrier function is very similar to one adopted on an heuristic basis.
Urea kinetic modeling: comparing the options.
Hoenich, N A; Keir, M J; Hildreth, K; Woffindin, C; Goodall, R; Vanholder, R; Ward, M K
1993-09-01
In this study 6 commercially produced kinetic modeling packages utilizing a variable volume, single pool urea model, as well as formulae to determine the delivery of therapy, have been compared by applying to each the same set of rigorously collected data for a group of 12 patients. Comparison of the kinetically derived parameters (urea generation rate [G], urea distribution volume [V], delivery of therapy [Kt/V], and normalized protein catabolic rate [nPCR]) showed that the values obtained for both G and V differed between packages owing to the numerical methods and the clearance used in the solution of the differential equations. Although a broad agreement between the values established for Kt/V and nPCR was noted, the 95% limits of agreement indicated that it would be prudent to exercise caution when comparing results established by different modeling packages. PMID:8240076
Modelling world gold prices and USD foreign exchange relationship using multivariate GARCH model
NASA Astrophysics Data System (ADS)
Ping, Pung Yean; Ahmad, Maizah Hura Binti
2014-12-01
World gold price is a popular investment commodity. The series have often been modeled using univariate models. The objective of this paper is to show that there is a co-movement between gold price and USD foreign exchange rate. Using the effect of the USD foreign exchange rate on the gold price, a model that can be used to forecast future gold prices is developed. For this purpose, the current paper proposes a multivariate GARCH (Bivariate GARCH) model. Using daily prices of both series from 01.01.2000 to 05.05.2014, a causal relation between the two series understudied are found and a bivariate GARCH model is produced.
Solution of the Black-Scholes Equation for Pricing of Barrier Option
NASA Astrophysics Data System (ADS)
Dehghan, Mehdi; Pourghanbar, Somayeh
2011-05-01
In this paper two different methods are presented to approximate the solution of the Black-Scholes equation for valuation of barrier option. These techniques can be applied directly for all types of differential equations, homogeneous or inhomogeneous. The use of these methods provides the solution of the problem in a closed form while the mesh point techniques provide the approximation at mesh points only. Also, the two schemes need less computational work in comparison with the traditional methods. These techniques can be employed for problems with initial condition. In this paper we use the variational iteration and homotopy perturbation methods for solving the Black-Scholes equation with terminal condition. Numerical results are compared with theoretical solutions in order to confirm the validity of the presented procedures.
Model Offices: Flexible Options, Local Innovations.
ERIC Educational Resources Information Center
Perspective: Essays and Reviews of Issues in Employment Security and Employment and Training Programs, 1990
1990-01-01
This volume of an annual journal contains 17 articles that focus on model local offices of the employment security (ES) and training systems. The articles are arranged in three parts. Part I, on developing new initiatives, contains the following five articles: "A Public Employment Service for the 1990s" (Elizabeth Dole); "The Revitalization of the…
Short-Term Energy Outlook Model Documentation: Regional Residential Heating Oil Price Model
2009-01-01
The regional residential heating oil price module of the Short-Term Energy Outlook (STEO) model is designed to provide residential retail price forecasts for the 4 census regions: Northeast, South, Midwest, and West.
Short-Term Energy Outlook Model Documentation: Regional Residential Propane Price Model
2009-01-01
The regional residential propane price module of the Short-Term Energy Outlook (STEO) model is designed to provide residential retail price forecasts for the 4 Census regions: Northeast, South, Midwest, and West.
Model documentation: Electricity market module, electricity finance and pricing submodule
Not Available
1994-04-07
The purpose of this report is to define the objectives of the model, describe its basic approach, and provide detail on how it works. The EFP is a regulatory accounting model that projects electricity prices. The model first solves for revenue requirements by building up a rate base, calculating a return on rate base, and adding the allowed expenses. Average revenues (prices) are calculated based on assumptions regarding regulator lag and customer cost allocation methods. The model then solves for the internal cash flow and analyzes the need for external financing to meet necessary capital expenditures. Finally, the EFP builds up the financial statements. The EFP is used in conjunction with the National Energy Modeling System (NEMS). Inputs to the EFP include the forecast generating capacity expansion plans, operating costs, regulator environment, and financial data. The outputs include forecasts of income statements, balance sheets, revenue requirements, and electricity prices.
Modeling of Solid Waste Processing Options in BIO-Plex
NASA Technical Reports Server (NTRS)
Rodriguez, Luis F.; Finn, Cory; Kang, Sukwon; Hogan, John; Luna, Bernadette (Technical Monitor)
2000-01-01
BIO-Plex is a ground-based test bed currently under development by NASA for testing technologies and practices that may be utilized in future long-term life support missions. All aspects of such an Advanced Life Support (ALS) System must be considered to confidently construct a reliable system, which will not only allow the crew to survive in harsh environments, but allow the crew time to perform meaningful research. Effective handling of solid wastes is a critical aspect of the system, especially when recovery of resources contained in the waste is required. This is particularly important for ALS Systems configurations that include a Biomass Production Chamber. In these cases, significant amounts of inedible biomass waste may be produced, which can ultimately serve as a repository of necessary resources for sustaining life, notably carbon, water, and plant nutrients. Numerous biological and physicochemical solid waste processing options have been considered. Biological options include composting, aerobic digestion, and anaerobic digestion. Physicochemical options include pyrolysis, SCWO (supercritical water oxidation), various incineration configurations, microwave incineration, magnetically assisted gasification, and low temperature plasma reaction. Modeling of these options is a necessary step to assist in the design process. A previously developed top-level model of BIO-Plex implemented in MATLAB Simulink (r) for the use of systems analysis and design has been adopted for this analysis. Presently, this model only considered incineration for solid waste processing. Present work, reported here, includes the expansion of this model to include a wider array of solid waste processing options selected from the above options, bearing in mind potential, near term solid waste treatment systems. Furthermore, a trade study has also been performed among these solid waste processing technologies in an effort to determine the ideal technology for long-term life support
Path integral approach to Asian options in the Black-Scholes model
NASA Astrophysics Data System (ADS)
Devreese, J. P. A.; Lemmens, D.; Tempere, J.
2010-02-01
We derive a closed-form solution for the price of an average strike as well as an average price geometric Asian option, by making use of the path integral formulation. Our results are compared to a numerical Monte Carlo simulation. We also develop a pricing formula for an Asian option with a barrier on a control process, combining the method of images with a partitioning of the set of paths according to the average along the path. This formula is exact when the correlation is zero, and is approximate when the correlation increases.
A quadranomial real options model for evaluation of emissions trading and technology
NASA Astrophysics Data System (ADS)
Sarkis, Joseph; Tamarkin, Maurry
2005-11-01
Green house gas (GHG) emissions have been tied to global climate change. One popular policy instrument that seems to have gained credibility with explicit mention of its application in the Kyoto Protocol is the use of permit trading and cap-and-trade mechanisms. Organizations functioning within this environment will need to manage their resources appropriately to remain competitive. Organizations will either have the opportunity to purchase emissions credits (offsets) from a market trading scheme or seek to reduce their emissions through different measures. Some measures may include investment in new technologies that will reduce their reliance on GHG emitting practices. In many countries, large organizations and institutions generate their own power to operate their facilities. Much of this power is generated (or bought) from GHG producing technology. Specific renewable energy sources such as wind and solar photovoltaic technology may become more feasible alternatives available to a large percentage of these organizations if they are able to take advantage and incorporate the market for GHG emissions trading in their analyses. To help organizations evaluate investment in these renewable energy technologies we introduce a real options based model that will take into consideration uncertainties associated with the technology and those associated with the GHG trading market. The real options analysis will consider both the stochastic (uncertainty) nature of the exercise price of the technology and the stochastic nature of the market trading price of the GHG emissions.
Modeling of price and profit in coupled-ring networks
NASA Astrophysics Data System (ADS)
Tangmongkollert, Kittiwat; Suwanna, Sujin
2016-06-01
We study the behaviors of magnetization, price, and profit profiles in ring networks in the presence of the external magnetic field. The Ising model is used to determine the state of each node, which is mapped to the buy-or-sell state in a financial market, where +1 is identified as the buying state, and -1 as the selling state. Price and profit mechanisms are modeled based on the assumption that price should increase if demand is larger than supply, and it should decrease otherwise. We find that the magnetization can be induced between two rings via coupling links, where the induced magnetization strength depends on the number of the coupling links. Consequently, the price behaves linearly with time, where its rate of change depends on the magnetization. The profit grows like a quadratic polynomial with coefficients dependent on the magnetization. If two rings have opposite direction of net spins, the price flows in the direction of the majority spins, and the network with the minority spins gets a loss in profit.
Pricing turbo warrants under mixed-exponential jump diffusion model
NASA Astrophysics Data System (ADS)
Yu, Jianfeng; Xu, Weidong
2016-06-01
Turbo warrant is a special type of barrier options in which the rebate is calculated as another exotic option. In this paper, using Laplace transforms we obtain the valuation of turbo warrant under the mixed-exponential jump diffusion model, which is able to approximate any jump size distribution. The numerical Laplace inversion examples verify that the analytical solutions are accurate. The results of simulation confirm the argument that jump risk should not be ignored in the valuation of turbo warrants.
Shabri, Ani; Samsudin, Ruhaidah
2014-01-01
Crude oil prices do play significant role in the global economy and are a key input into option pricing formulas, portfolio allocation, and risk measurement. In this paper, a hybrid model integrating wavelet and multiple linear regressions (MLR) is proposed for crude oil price forecasting. In this model, Mallat wavelet transform is first selected to decompose an original time series into several subseries with different scale. Then, the principal component analysis (PCA) is used in processing subseries data in MLR for crude oil price forecasting. The particle swarm optimization (PSO) is used to adopt the optimal parameters of the MLR model. To assess the effectiveness of this model, daily crude oil market, West Texas Intermediate (WTI), has been used as the case study. Time series prediction capability performance of the WMLR model is compared with the MLR, ARIMA, and GARCH models using various statistics measures. The experimental results show that the proposed model outperforms the individual models in forecasting of the crude oil prices series. PMID:24895666
Shabri, Ani; Samsudin, Ruhaidah
2014-01-01
Crude oil prices do play significant role in the global economy and are a key input into option pricing formulas, portfolio allocation, and risk measurement. In this paper, a hybrid model integrating wavelet and multiple linear regressions (MLR) is proposed for crude oil price forecasting. In this model, Mallat wavelet transform is first selected to decompose an original time series into several subseries with different scale. Then, the principal component analysis (PCA) is used in processing subseries data in MLR for crude oil price forecasting. The particle swarm optimization (PSO) is used to adopt the optimal parameters of the MLR model. To assess the effectiveness of this model, daily crude oil market, West Texas Intermediate (WTI), has been used as the case study. Time series prediction capability performance of the WMLR model is compared with the MLR, ARIMA, and GARCH models using various statistics measures. The experimental results show that the proposed model outperforms the individual models in forecasting of the crude oil prices series. PMID:24895666
A Model of Price Search Behavior in Electronic Marketplace.
ERIC Educational Resources Information Center
Jiang, Pingjun
2002-01-01
Discussion of online consumer behavior focuses on the development of a conceptual model and a set of propositions to explain the main factors influencing online price search. Integrates the psychological search literature into the context of online searching by incorporating ability and cost to search for information into perceived search…
Pricing Models for Electronic Databases on the Internet.
ERIC Educational Resources Information Center
Machovec, George S., Ed.
1998-01-01
Outlines prevalent electronic information pricing models along with their strengths and weaknesses. Highlights include full-time equivalent (FTE) student counts; pure head counts; print plus fee; concurrent users; IP (information provider) classes; by transaction, connect time or retrieval; other factors, e.g., total budget and materials budget;…
Application for Single Price Auction Model (SPA) in AC Network
NASA Astrophysics Data System (ADS)
Wachi, Tsunehisa; Fukutome, Suguru; Chen, Luonan; Makino, Yoshinori; Koshimizu, Gentarou
This paper aims to develop a single price auction model with AC transmission network, based on the principle of maximizing social surplus of electricity market. Specifically, we first formulate the auction market as a nonlinear optimization problem, which has almost the same form as the conventional optimal power flow problem, and then propose an algorithm to derive both market clearing price and trade volume of each player even for the case of market-splitting. As indicated in the paper, the proposed approach can be used not only for the price evaluation of auction or bidding market but also for analysis of bidding strategy, congestion effect and other constraints or factors. Several numerical examples are used to demonstrate effectiveness of our method.
Valuing water resources in Switzerland using a hedonic price model
NASA Astrophysics Data System (ADS)
van Dijk, Diana; Siber, Rosi; Brouwer, Roy; Logar, Ivana; Sanadgol, Dorsa
2016-05-01
In this paper, linear and spatial hedonic price models are applied to the housing market in Switzerland, covering all 26 cantons in the country over the period 2005-2010. Besides structural house, neighborhood and socioeconomic characteristics, we include a wide variety of new environmental characteristics related to water to examine their role in explaining variation in sales prices. These include water abundance, different types of water bodies, the recreational function of water, and water disamenity. Significant spatial autocorrelation is found in the estimated models, as well as nonlinear effects for distances to the nearest lake and large river. Significant effects are furthermore found for water abundance and the distance to large rivers, but not to small rivers. Although in both linear and spatial models water related variables explain less than 1% of the price variation, the distance to the nearest bathing site has a larger marginal contribution than many neighborhood-related distance variables. The housing market shows to differentiate between different water related resources in terms of relative contribution to house prices, which could help the housing development industry make more geographically targeted planning activities.
A stochastic delay model for pricing debt and equity: Numerical techniques and applications
NASA Astrophysics Data System (ADS)
Tambue, Antoine; Kemajou Brown, Elisabeth; Mohammed, Salah
2015-01-01
Delayed nonlinear models for pricing corporate liabilities and European options were recently developed. Using self-financed strategy and duplication we were able to derive a Random Partial Differential Equation (RPDE) whose solutions describe the evolution of debt and equity values of a corporate in the last delay period interval in the accompanied paper (Kemajou et al., 2012) [14]. In this paper, we provide robust numerical techniques to solve the delayed nonlinear model for the corporate value, along with the corresponding RPDEs modeling the debt and equity values of the corporate. Using financial data from some firms, we forecast and compare numerical solutions from both the nonlinear delayed model and classical Merton model with the real corporate data. From this comparison, it comes up that in corporate finance the past dependence of the firm value process may be an important feature and therefore should not be ignored.
A discontinuous Galerkin method for two-dimensional PDE models of Asian options
NASA Astrophysics Data System (ADS)
Hozman, J.; Tichý, T.; Cvejnová, D.
2016-06-01
In our previous research we have focused on the problem of plain vanilla option valuation using discontinuous Galerkin method for numerical PDE solution. Here we extend a simple one-dimensional problem into two-dimensional one and design a scheme for valuation of Asian options, i.e. options with payoff depending on the average of prices collected over prespecified horizon. The algorithm is based on the approach combining the advantages of the finite element methods together with the piecewise polynomial generally discontinuous approximations. Finally, an illustrative example using DAX option market data is provided.
Meier, Petra S.; Holmes, John; Angus, Colin; Ally, Abdallah K.; Meng, Yang; Brennan, Alan
2016-01-01
Introduction While evidence that alcohol pricing policies reduce alcohol-related health harm is robust, and alcohol taxation increases are a WHO “best buy” intervention, there is a lack of research comparing the scale and distribution across society of health impacts arising from alternative tax and price policy options. The aim of this study is to test whether four common alcohol taxation and pricing strategies differ in their impact on health inequalities. Methods and Findings An econometric epidemiological model was built with England 2014/2015 as the setting. Four pricing strategies implemented on top of the current tax were equalised to give the same 4.3% population-wide reduction in total alcohol-related mortality: current tax increase, a 13.4% all-product duty increase under the current UK system; a value-based tax, a 4.0% ad valorem tax based on product price; a strength-based tax, a volumetric tax of £0.22 per UK alcohol unit (= 8 g of ethanol); and minimum unit pricing, a minimum price threshold of £0.50 per unit, below which alcohol cannot be sold. Model inputs were calculated by combining data from representative household surveys on alcohol purchasing and consumption, administrative and healthcare data on 43 alcohol-attributable diseases, and published price elasticities and relative risk functions. Outcomes were annual per capita consumption, consumer spending, and alcohol-related deaths. Uncertainty was assessed via partial probabilistic sensitivity analysis (PSA) and scenario analysis. The pricing strategies differ as to how effects are distributed across the population, and, from a public health perspective, heavy drinkers in routine/manual occupations are a key group as they are at greatest risk of health harm from their drinking. Strength-based taxation and minimum unit pricing would have greater effects on mortality among drinkers in routine/manual occupations (particularly for heavy drinkers, where the estimated policy effects on
Federal Register 2010, 2011, 2012, 2013, 2014
2010-10-26
..., 2010. The closing price for SIRI on that day was $ 0.9678. If the investor wanted to buy a call option... contract times 50 contracts). \\6\\ Using a Black Scholes pricing model. Similarly, if an investor wanted...
The asset pricing model of musharakah factors
NASA Astrophysics Data System (ADS)
Simon, Shahril; Omar, Mohd; Lazam, Norazliani Md
2015-02-01
The existing three-factor model developed by Fama and French for conventional investment was formulated based on risk-free rates element in which contradict with Shariah principles. We note that the underlying principles that govern Shariah investment were mutual risk and profit sharing between parties, the assurance of fairness for all and that transactions were based on an underlying asset. In addition, the three-factor model did not exclude stock that was not permissible by Shariah such as financial services based on riba (interest), gambling operator, manufacture or sale of non-halal products or related products and other activities deemed non-permissible according to Shariah. Our approach to construct the factor model for Shariah investment was based on the basic tenets of musharakah in tabulating the factors. We start by noting that Islamic stocks with similar characteristics should have similar returns and risks. This similarity between Islamic stocks was defined by the similarity of musharakah attributes such as business, management, profitability and capital. These attributes define factor exposures (or betas) to factors. The main takeaways were that musharakah attributes we chose had explain stock returns well in cross section and were significant in different market environments. The management factor seemed to be responsible for the general dynamics of the explanatory power.
Modeling of materials supply, demand and prices
NASA Technical Reports Server (NTRS)
1982-01-01
The societal, economic, and policy tradeoffs associated with materials processing and utilization, are discussed. The materials system provides the materials engineer with the system analysis required for formulate sound materials processing, utilization, and resource development policies and strategies. Materials system simulation and modeling research program including assessments of materials substitution dynamics, public policy implications, and materials process economics was expanded. This effort includes several collaborative programs with materials engineers, economists, and policy analysts. The technical and socioeconomic issues of materials recycling, input-output analysis, and technological change and productivity are examined. The major thrust areas in materials systems research are outlined.
Adaptation of warrant price with Black Scholes model and historical volatility
NASA Astrophysics Data System (ADS)
Aziz, Khairu Azlan Abd; Idris, Mohd Fazril Izhar Mohd; Saian, Rizauddin; Daud, Wan Suhana Wan
2015-05-01
This project discusses about pricing warrant in Malaysia. The Black Scholes model with non-dividend approach and linear interpolation technique was applied in pricing the call warrant. Three call warrants that are listed in Bursa Malaysia were selected randomly from UiTM's datastream. The finding claims that the volatility for each call warrants are different to each other. We have used the historical volatility which will describes the price movement by which an underlying share is expected to fluctuate within a period. The Black Scholes model price that was obtained by the model will be compared with the actual market price. Mispricing the call warrants will contribute to under or over valuation price. Other variables like interest rate, time to maturity date, exercise price and underlying stock price are involves in pricing call warrants as well as measuring the moneyness of call warrants.
Slice sampling technique in Bayesian extreme of gold price modelling
NASA Astrophysics Data System (ADS)
Rostami, Mohammad; Adam, Mohd Bakri; Ibrahim, Noor Akma; Yahya, Mohamed Hisham
2013-09-01
In this paper, a simulation study of Bayesian extreme values by using Markov Chain Monte Carlo via slice sampling algorithm is implemented. We compared the accuracy of slice sampling with other methods for a Gumbel model. This study revealed that slice sampling algorithm offers more accurate and closer estimates with less RMSE than other methods . Finally we successfully employed this procedure to estimate the parameters of Malaysia extreme gold price from 2000 to 2011.
Short-Term Energy Outlook Model Documentation: Petroleum Product Prices Module
2015-01-01
The petroleum products price module of the Short-Term Energy Outlook (STEO) model is designed to provide U.S. average wholesale and retail price forecasts for motor gasoline, diesel fuel, heating oil, and jet fuel.
Path Integrals and Exotic Options:. Methods and Numerical Results
NASA Astrophysics Data System (ADS)
Bormetti, G.; Montagna, G.; Moreni, N.; Nicrosini, O.
2005-09-01
In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price path dependent options on multidimensional and correlated underlying assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the case of Asian call options. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at the money (ATM) and out of the money (OTM) options, path integral exhibits competitive performances.
Pricing of medical devices under coverage uncertainty--a modelling approach.
Girling, Alan J; Lilford, Richard J; Young, Terry P
2012-12-01
Product vendors and manufacturers are increasingly aware that purchasers of health care will fund new clinical treatments only if they are perceived to deliver value-for-money. This influences companies' internal commercial decisions, including the price they set for their products. Other things being equal, there is a price threshold, which is the maximum price at which the device will be funded and which, if its value were known, would play a central role in price determination. This paper examines the problem of pricing a medical device from the vendor's point of view in the presence of uncertainty about what the price threshold will be. A formal solution is obtained by maximising the expected value of the net revenue function, assuming a Bayesian prior distribution for the price threshold. A least admissible price is identified. The model can also be used as a tool for analysing proposed pricing policies when no formal prior specification of uncertainty is available. PMID:22021085
Theory of Financial Risk and Derivative Pricing
NASA Astrophysics Data System (ADS)
Bouchaud, Jean-Philippe; Potters, Marc
2009-01-01
Foreword; Preface; 1. Probability theory: basic notions; 2. Maximum and addition of random variables; 3. Continuous time limit, Ito calculus and path integrals; 4. Analysis of empirical data; 5. Financial products and financial markets; 6. Statistics of real prices: basic results; 7. Non-linear correlations and volatility fluctuations; 8. Skewness and price-volatility correlations; 9. Cross-correlations; 10. Risk measures; 11. Extreme correlations and variety; 12. Optimal portfolios; 13. Futures and options: fundamental concepts; 14. Options: hedging and residual risk; 15. Options: the role of drift and correlations; 16. Options: the Black and Scholes model; 17. Options: some more specific problems; 18. Options: minimum variance Monte-Carlo; 19. The yield curve; 20. Simple mechanisms for anomalous price statistics; Index of most important symbols; Index.
Short-Term Energy Outlook Model Documentation: Natural Gas Consumption and Prices
2015-01-01
The natural gas consumption and price modules of the Short-Term Energy Outlook (STEO) model are designed to provide consumption and end-use retail price forecasts for the residential, commercial, and industrial sectors in the nine Census districts and natural gas working inventories in three regions. Natural gas consumption shares and prices in each Census district are used to calculate an average U.S. retail price for each end-use sector.
Federal Register 2010, 2011, 2012, 2013, 2014
2011-05-10
... Register of December 8, 2010 (75 FR 76472) (December 2010 notice), FDA issued a notice to request that... associations representing such companies. (See 75 FR 61497, October 5, 2010.) Based on comments submitted to... HUMAN SERVICES Food and Drug Administration Biologics Price Competition and Innovation Act of...
The valuation of currency options by fractional Brownian motion.
Shokrollahi, Foad; Kılıçman, Adem
2016-01-01
This research aims to investigate a model for pricing of currency options in which value governed by the fractional Brownian motion model (FBM). The fractional partial differential equation and some Greeks are also obtained. In addition, some properties of our pricing formula and simulation studies are presented, which demonstrate that the FBM model is easy to use. PMID:27504243
Modeling Long-term Behavior of Stock Market Prices Using Differential Equations
NASA Astrophysics Data System (ADS)
Yang, Xiaoxiang; Zhao, Conan; Mazilu, Irina
2015-03-01
Due to incomplete information available in the market and uncertainties associated with the price determination process, the stock prices fluctuate randomly during a short period of time. In the long run, however, certain economic factors, such as the interest rate, the inflation rate, and the company's revenue growth rate, will cause a gradual shift in the stock price. Thus, in this paper, a differential equation model has been constructed in order to study the effects of these factors on the stock prices. The model obtained accurately describes the general trends in the AAPL and XOM stock price changes over the last ten years.
Interest rates in quantum finance: Caps, swaptions and bond options
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.
2010-01-01
The prices of the main interest rate options in the financial markets, derived from the Libor (London Interbank Overnight Rate), are studied in the quantum finance model of interest rates. The option prices show new features for the Libor Market Model arising from the fact that, in the quantum finance formulation, all the different Libor payments are coupled and (imperfectly) correlated. Black’s caplet formula for quantum finance is given an exact path integral derivation. The coupon and zero coupon bond options as well as the Libor European and Asian swaptions are derived in the framework of quantum finance. The approximate Libor option prices are derived using the volatility expansion. The BGM-Jamshidian (Gatarek et al. (1996) [1], Jamshidian (1997) [2]) result for the Libor swaption prices is obtained as the limiting case when all the Libors are exactly correlated. A path integral derivation is given of the approximate BGM-Jamshidian approximate price.
Developing a new stochastic competitive model regarding inventory and price
NASA Astrophysics Data System (ADS)
Rashid, Reza; Bozorgi-Amiri, Ali; Seyedhoseini, S. M.
2015-01-01
Within the competition in today's business environment, the design of supply chains becomes more complex than before. This paper deals with the retailer's location problem when customers choose their vendors, and inventory costs have been considered for retailers. In a competitive location problem, price and location of facilities affect demands of customers; consequently, simultaneous optimization of the location and inventory system is needed. To prepare a realistic model, demand and lead time have been assumed as stochastic parameters, and queuing theory has been used to develop a comprehensive mathematical model. Due to complexity of the problem, a branch and bound algorithm has been developed, and its performance has been validated in several numerical examples, which indicated effectiveness of the algorithm. Also, a real case has been prepared to demonstrate performance of the model for real world.
A semi-Markov model for price returns
NASA Astrophysics Data System (ADS)
D'Amico, Guglielmo; Petroni, Filippo
2012-10-01
We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday returns are described by a discrete time homogeneous semi-Markov process and the overnight returns are modeled by a Markov chain. Based on this assumptions we derived the equations for the first passage time distribution and the volatility autocorrelation function. Theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from 1 January 2007 until the end of December 2010. The semi-Markov hypothesis is also tested through a nonparametric test of hypothesis.
Cooperative and non-cooperative discrete differential models of oil pricing and the OPEC cartel
Ahmadian, M.
1984-01-01
The theoretical purpose of the study is to determine and to compare the oil price paths for different market structures, which include cooperative and non-cooperative discrete differential models of the world oil market. The latter (NCDDMs) includes competitive, monopolistic, and Nash-Cournot markets; whereas, the former consists of a Nash-bargaining model (NBM). The empirical purpose of the study are: 1) to apply the NBM to the world oil market and evaluate the OPEC behavior as a price-maker, 2) to elaborate the implications of oil price rises on OPEC cartel stability, and 3) to show how restrictions on production are allocated among OPEC nations. In the monopolistic and competitive markets, under the assumptions of constant production costs over time and identical discount rates, the study concludes that when the initial monopoly price is higher than (lower than) the initial competitive price, the optimal monopoly price path with increasing (decreasing) oil demand elasticities over time will intersect the optimal competitive price path. Also, the optimal monopoly price path with constant oil demand elasticities over time will continue along and be identical and parallel to the competitive price path, whether the initial monopoly price is equal to or different from the inital competitive price.
Kinetic market models with single commodity having price fluctuations
NASA Astrophysics Data System (ADS)
Chatterjee, A.; Chakrabarti, B. K.
2006-12-01
We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of trading or exchange of money and commodity proceeds, with local (in time) fluctuations in the price of the commodity. These distributions are studied in markets with agents having uniform and random saving factors. The self-organizing features in money distribution are similar to the cases without any commodity (or with consumable commodities), while the commodity distribution shows an exponential decay. The wealth distribution shows interesting behavior: gamma like distribution for uniform saving propensity and has the same power-law tail, as that of the money distribution, for a market with agents having random saving propensity.
Quantum spatial-periodic harmonic model for daily price-limited stock markets
NASA Astrophysics Data System (ADS)
Meng, Xiangyi; Zhang, Jian-Wei; Xu, Jingjing; Guo, Hong
2015-11-01
We investigate the behaviors of stocks in daily price-limited stock markets by purposing a quantum spatial-periodic harmonic model. The stock price is considered to be oscillating and damping in a quantum spatial-periodic harmonic oscillator potential well. A complicated non-linear relation including inter-band positive correlation and intra-band negative correlation between the volatility and trading volume of a stock is numerically derived with the energy band structure of the model concerned. The effectiveness of price limit is re-examined, with some observed characteristics of price-limited stock markets in China studied by applying our quantum model.
Numerical valuation of discrete double barrier options
NASA Astrophysics Data System (ADS)
Milev, Mariyan; Tagliani, Aldo
2010-03-01
In the present paper we explore the problem for pricing discrete barrier options utilizing the Black-Scholes model for the random movement of the asset price. We postulate the problem as a path integral calculation by choosing approach that is similar to the quadrature method. Thus, the problem is reduced to the estimation of a multi-dimensional integral whose dimension corresponds to the number of the monitoring dates. We propose a fast and accurate numerical algorithm for its valuation. Our results for pricing discretely monitored one and double barrier options are in agreement with those obtained by other numerical and analytical methods in Finance and literature. A desired level of accuracy is very fast achieved for values of the underlying asset close to the strike price or the barriers. The method has a simple computer implementation and it permits observing the entire life of the option.
Preliminary analysis on hybrid Box-Jenkins - GARCH modeling in forecasting gold price
NASA Astrophysics Data System (ADS)
Yaziz, Siti Roslindar; Azizan, Noor Azlinna; Ahmad, Maizah Hura; Zakaria, Roslinazairimah; Agrawal, Manju; Boland, John
2015-02-01
Gold has been regarded as a valuable precious metal and the most popular commodity as a healthy return investment. Hence, the analysis and prediction of gold price become very significant to investors. This study is a preliminary analysis on gold price and its volatility that focuses on the performance of hybrid Box-Jenkins models together with GARCH in analyzing and forecasting gold price. The Box-Cox formula is used as the data transformation method due to its potential best practice in normalizing data, stabilizing variance and reduces heteroscedasticity using 41-year daily gold price data series starting 2nd January 1973. Our study indicates that the proposed hybrid model ARIMA-GARCH with t-innovation can be a new potential approach in forecasting gold price. This finding proves the strength of GARCH in handling volatility in the gold price as well as overcomes the non-linear limitation in the Box-Jenkins modeling.
Assessment of the dynamics of Asian and European option on the hybrid system
NASA Astrophysics Data System (ADS)
Bogdanov, A. V.; Stepanov, E. A.; Khmel, D. S.
2016-02-01
In this article the problem of performance optimization for estimation of European and Asian options pricing is discussed. The main goal is to substantially improve the performance in solving the problems on the hybrid system. The authors optimized the algorithms of the Monte Carlo method for solving stochastic differential equations and path integral derived from Black-Scholes model for pricing options.
NASA Astrophysics Data System (ADS)
Daniels, Marcus G.; Farmer, J. Doyne; Gillemot, László; Iori, Giulia; Smith, Eric
2003-03-01
We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices.
Daniels, Marcus G; Farmer, J Doyne; Gillemot, László; Iori, Giulia; Smith, Eric
2003-03-14
We model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties of markets, such as the diffusion rate of prices (which is the standard measure of financial risk) and the spread and price impact functions (which are the main determinants of transaction cost). Guided by dimensional analysis, simulation, and mean-field theory, we find scaling relations in terms of order flow rates. We show that even under completely random order flow the need to store supply and demand to facilitate trading induces anomalous diffusion and temporal structure in prices. PMID:12689037
A Bayesian Multi-Level Factor Analytic Model of Consumer Price Sensitivities across Categories
ERIC Educational Resources Information Center
Duvvuri, Sri Devi; Gruca, Thomas S.
2010-01-01
Identifying price sensitive consumers is an important problem in marketing. We develop a Bayesian multi-level factor analytic model of the covariation among household-level price sensitivities across product categories that are substitutes. Based on a multivariate probit model of category incidence, this framework also allows the researcher to…
Price of oil and OPEC behavior: a utility maximization model
Adeinat, M.K.
1985-01-01
There is growing evidence that OPEC has neither behaved as a cartel, at least in the last decade, nor maximized the discounted value of its profits as would be suggested by the theory of exhaustible resources. This dissertation attempts to find a way out of this dead end by proposing a utility maximization model. According to the utility maximization model, the decisions of how much crude oil each country produces is determined by a country's budgetary needs. The objective of each country is to choose present consumption and future consumption (which must be financed by its future income which can, in turn, be generated either by its investment out of current income or the proceeds of its oil reserves) at time t to maximize its utility function subject to its budget and absorptive capacity constraints. The model predicted that whenever the amount of savings is greater than the country's absorptive capacity as a result of higher prices of oil, it would respond by cutting back its production of oil. This prediction is supported by the following empirical findings: (1) that the marginal propensity to save (MPS) exceeded the marginal propensity to invest (MPI) during the period of study (1967-1981), implying that OPEC countries were facing an absorptive capacity constraint and (2) the quantity of oil production responded negatively to the permanent income in all three countries, the response being highly significant for those countries with the greatest budget surpluses.
Maximum entropy distribution of stock price fluctuations
NASA Astrophysics Data System (ADS)
Bartiromo, Rosario
2013-04-01
In this paper we propose to use the principle of absence of arbitrage opportunities in its entropic interpretation to obtain the distribution of stock price fluctuations by maximizing its information entropy. We show that this approach leads to a physical description of the underlying dynamics as a random walk characterized by a stochastic diffusion coefficient and constrained to a given value of the expected volatility, in this way taking into account the information provided by the existence of an option market. The model is validated by a comprehensive comparison with observed distributions of both price return and diffusion coefficient. Expected volatility is the only parameter in the model and can be obtained by analysing option prices. We give an analytic formulation of the probability density function for price returns which can be used to extract expected volatility from stock option data.
The Conquest of Outer Space--Optional Curriculum Model
ERIC Educational Resources Information Center
Florian, Gabriel; Florian, Aurelia-Daniela; Pufu, Nicolae
2015-01-01
This paper proposes an optional syllabus for the students in the XIIth grade. The proposed theme analyzes the concept of "variable mass" both in terms of classical mechanics and relativistic mechanics. In terms of classical mechanics we refer to the slow motion of a body, whose mass ranges in ascending way (by annealing a mass particle…
Comparison of two water pricing policies in hydro-economic modeling study
NASA Astrophysics Data System (ADS)
Riegels, N.; Pulido Velazquez, M.; Doulgeris, C.; Sturm, V.; Jensen, R.; Møller, F.; Bauer-Gottwein, P.
2012-04-01
A study is presented comparing two different water pricing policies that are applied to wholesale water users throughout a river basin. The purpose of the study is to test policies that meet some of the water pricing objectives of the European Union Water Framework Directive (WFD). In the first policy, a single volumetric water price is applied to all wholesale water users throughout a case study river basin located in northern Greece. The same price is applied consistently to all surface water and groundwater users regardless of water use type and does not vary in space or time. In the second policy surface water is priced at a uniform volumetric price, while groundwater is priced using the price of energy as a surrogate for a volumetric water price. The policies are compared using a hydro-economic modeling approach in which wholesale water users are assumed to respond to water price changes according to microeconomic theory. A hydrological model of the case study river basin is used to estimate the impact of water use changes on river flow patterns, which are then used to assess the ecological status of the basin. WFD ecological status requirements are imposed as a constraint in the model, and an optimization approach is used to identify prices that meet the WFD requirements while minimizing opportunity costs (in terms of total welfare losses). Model results suggest that there is little difference between the two approaches in terms of the total opportunity costs of meeting the ecological status requirements of the WFD. However, the distribution of opportunity costs is different, with the second approach reducing the economic impact on producers of low value crops and small urban/domestic users. Because growers of low value crops will suffer the most from water price increases, the second policy offers the advantage of reducing this burden. In addition, because of difficulties associated with monitoring groundwater use, the second policy may be easier to
Bouchard, Bruno Vu, Thanh Nam
2010-04-15
We provide an obstacle version of the Geometric Dynamic Programming Principle of Soner and Touzi (J. Eur. Math. Soc. 4:201-236, 2002) for stochastic target problems. This opens the doors to a wide range of applications, particularly in risk control in finance and insurance, in which a controlled stochastic process has to be maintained in a given set on a time interval [0,T]. As an example of application, we show how it can be used to provide a viscosity characterization of the super-hedging cost of American options under portfolio constraints, without appealing to the standard dual formulation from mathematical finance. In particular, we allow for a degenerate volatility, a case which does not seem to have been studied so far in this context.
A GIS-based hedonic price model for agricultural land
NASA Astrophysics Data System (ADS)
Demetriou, Demetris
2015-06-01
Land consolidation is a very effective land management planning approach that aims towards rural/agricultural sustainable development. Land reallocation which involves land tenure restructuring is the most important, complex and time consuming component of land consolidation. Land reallocation relies on land valuation since its fundamental principle provides that after consolidation, each landowner shall be granted a property of an aggregate value that is approximately the same as the value of the property owned prior to consolidation. Therefore, land value is the crucial factor for the land reallocation process and hence for the success and acceptance of the final land consolidation plan. Land valuation is a process of assigning values to all parcels (and its contents) and it is usually carried out by an ad-hoc committee. However, the process faces some problems such as it is time consuming hence costly, outcomes may present inconsistency since it is carried out manually and empirically without employing systematic analytical tools and in particular spatial analysis tools and techniques such as statistical/mathematical. A solution to these problems can be the employment of mass appraisal land valuation methods using automated valuation models (AVM) based on international standards. In this context, this paper presents a spatial based linear hedonic price model which has been developed and tested in a case study land consolidation area in Cyprus. Results showed that the AVM is capable to produce acceptable in terms of accuracy and reliability land values and to reduce time hence cost required by around 80%.
Delta hedged option valuation with underlying non-Gaussian returns
NASA Astrophysics Data System (ADS)
Moriconi, L.
2007-07-01
The standard Black-Scholes theory of option pricing is extended to cope with underlying return fluctuations described by general probability distributions. A Langevin process and its related Fokker-Planck equation are devised to model the market stochastic dynamics, allowing us to write and formally solve the generalized Black-Scholes equation implied by dynamical hedging. A systematic expansion around a non-perturbative starting point is then implemented, recovering the Matacz's conjectured option pricing expression. We perform an application of our formalism to the real stock market and find clear evidence that while past financial time series can be used to evaluate option prices before the expiry date with reasonable accuracy, the stochastic character of volatility is an essential ingredient that should necessarily be taken into account in analytical option price modeling.
Equilibrium pricing in an order book environment: Case study for a spin model
NASA Astrophysics Data System (ADS)
Meudt, Frederik; Schmitt, Thilo A.; Schäfer, Rudi; Guhr, Thomas
2016-07-01
When modeling stock market dynamics, the price formation is often based on an equilibrium mechanism. In real stock exchanges, however, the price formation is governed by the order book. It is thus interesting to check if the resulting stylized facts of a model with equilibrium pricing change, remain the same or, more generally, are compatible with the order book environment. We tackle this issue in the framework of a case study by embedding the Bornholdt-Kaizoji-Fujiwara spin model into the order book dynamics. To this end, we use a recently developed agent based model that realistically incorporates the order book. We find realistic stylized facts. We conclude for the studied case that equilibrium pricing is not needed and that the corresponding assumption of a "fundamental" price may be abandoned.
Adaptive hidden Markov model with anomaly States for price manipulation detection.
Cao, Yi; Li, Yuhua; Coleman, Sonya; Belatreche, Ammar; McGinnity, Thomas Martin
2015-02-01
Price manipulation refers to the activities of those traders who use carefully designed trading behaviors to manually push up or down the underlying equity prices for making profits. With increasing volumes and frequency of trading, price manipulation can be extremely damaging to the proper functioning and integrity of capital markets. The existing literature focuses on either empirical studies of market abuse cases or analysis of particular manipulation types based on certain assumptions. Effective approaches for analyzing and detecting price manipulation in real time are yet to be developed. This paper proposes a novel approach, called adaptive hidden Markov model with anomaly states (AHMMAS) for modeling and detecting price manipulation activities. Together with wavelet transformations and gradients as the feature extraction methods, the AHMMAS model caters to price manipulation detection and basic manipulation type recognition. The evaluation experiments conducted on seven stock tick data from NASDAQ and the London Stock Exchange and 10 simulated stock prices by stochastic differential equation show that the proposed AHMMAS model can effectively detect price manipulation patterns and outperforms the selected benchmark models. PMID:25608293
The impact of energy pricing policy on Taiwan`s economy: A simulation of CGE model
Bor, Y.J.
1995-12-31
The purpose of this paper is to simulate the impacts of energy pricing policy on Taiwan`s economy. Based on a CGE model and utilizing empirical data from the 1989 input-output table, energy balance table and the national income report of Taiwan, this paper simulates a single energy price shock, witch is a 1 percent increase in one energy commodity, and examines two real cases of energy price adjustment, on February 16 and August 10, 1994 (a decrease of about 3 percent and an increase of about 3 percent in oil and gas prices). The simulation results are then interpreted. Finally, the conclusion and suggestions for further research are presented.
[Exploration of influencing factors of price of herbal based on VAR model].
Wang, Nuo; Liu, Shu-Zhen; Yang, Guang
2014-10-01
Based on vector auto-regression (VAR) model, this paper takes advantage of Granger causality test, variance decomposition and impulse response analysis techniques to carry out a comprehensive study of the factors influencing the price of Chinese herbal, including herbal cultivation costs, acreage, natural disasters, the residents' needs and inflation. The study found that there is Granger causality relationship between inflation and herbal prices, cultivation costs and herbal prices. And in the total variance analysis of Chinese herbal and medicine price index, the largest contribution to it is from its own fluctuations, followed by the cultivation costs and inflation. PMID:25751965
Introducing a price variation limiter mechanism into a behavioral financial market model.
Naimzada, Ahmad; Pireddu, Marina
2015-08-01
In the present paper, we consider a nonlinear financial market model in which, in order to decrease the complexity of the dynamics and to achieve price stabilization, we introduce a price variation limiter mechanism, which in each period bounds the price variation so that the current price is forced to belong to a certain interval determined by the price realization in the previous period. More precisely, we introduce such mechanism into a financial market model in which the price dynamics are described by a sigmoidal price adjustment mechanism characterized by the presence of two asymptotes that bound the price variation and thus the dynamics. We show that the presence of our asymptotes prevents divergence and negativity issues. Moreover, we prove that the basins of attraction are complicated only under suitable conditions on the parameters and that chaos arises just when the price limiters are loose enough. On the other hand, for some suitable parameter configurations, we detect multistability phenomena characterized by the presence of up to three coexisting attractors. PMID:26328563
Introducing a price variation limiter mechanism into a behavioral financial market model
NASA Astrophysics Data System (ADS)
Naimzada, Ahmad; Pireddu, Marina
2015-08-01
In the present paper, we consider a nonlinear financial market model in which, in order to decrease the complexity of the dynamics and to achieve price stabilization, we introduce a price variation limiter mechanism, which in each period bounds the price variation so that the current price is forced to belong to a certain interval determined by the price realization in the previous period. More precisely, we introduce such mechanism into a financial market model in which the price dynamics are described by a sigmoidal price adjustment mechanism characterized by the presence of two asymptotes that bound the price variation and thus the dynamics. We show that the presence of our asymptotes prevents divergence and negativity issues. Moreover, we prove that the basins of attraction are complicated only under suitable conditions on the parameters and that chaos arises just when the price limiters are loose enough. On the other hand, for some suitable parameter configurations, we detect multistability phenomena characterized by the presence of up to three coexisting attractors.
NASA Astrophysics Data System (ADS)
Jiang, C.; Fang, H.
2012-12-01
Modeling soil reflectance is important to describe the soil-vegetation radiation field and to retrieve canopy characteristics from remote sensing data. The Price soil reflectance model has been widely used in canopy reflectance modeling thanks to its simplicity and effectiveness. In order to improve the model generality and applicability, this study refines the Price soil reflectance model using a global spectral library and further proposes a novel soil reflectance model. The global soil spectral library was combined from six datasets, containing 6,971 soil samples around the world, with a 10nm interval from 450 to 2350 nm. A recalibrated Price model (CPM) was developed using the same algorithm used by standard Price model (SPM) to obtain globally representative fitting functions. Moreover, a new matrix decomposition method (MDM) was developed to decrease the reflectance simulation errors by considering the spectra curve shapes. Three tune parameters are sufficient to model global soil spectra using MDM, which achieves the highest accuracy with an absolute error less than 0.02 and relative error less than 5%. CPM and SPM have larger simulation errors, for which the RMSE/RRMSE are 0.029/7.5% and 0.068/16.8%, respectively. For both SPM and CPM, relatively large error variations are shown over wavelengths, because only three selected bands are used in the models. MDM exhibits a relatively stable performance in the whole spectral domain. Moreover, MDM reconstructs very well the general shapes of the five types of soil reflectance curves, and thus leads to a lower misclassification rate. Overall, both CPM and MDM outperform SPM and have a potential for global soil reflectance modeling. Density scatter plots between the measured reflectances in the global soil spectral library and the simulated reflectances using SPM (a), CPM (b) and MDM (c). Comparison of measured and simulated reflectances for five typical curves.
A BEHAVIORAL ECONOMIC MODEL OF ALCOHOL ADVERTISING AND PRICE
SAFFER, HENRY; DAVE, DHAVAL; GROSSMAN, MICHAEL
2016-01-01
SUMMARY This paper presents a new empirical study of the effects of televised alcohol advertising and alcohol price on alcohol consumption. A novel feature of this study is that the empirical work is guided by insights from behavioral economic theory. Unlike the theory used in most prior studies, this theory predicts that restriction on alcohol advertising on TV would be more effective in reducing consumption for individuals with high consumption levels but less effective for individuals with low consumption levels. The estimation work employs data from the National Longitudinal Survey of Youth, and the empirical model is estimated with quantile regressions. The results show that advertising has a small positive effect on consumption and that this effect is relatively larger at high consumption levels. The continuing importance of alcohol taxes is also supported. Education is employed as a proxy for self-regulation, and the results are consistent with this assumption. The key conclusion is that restrictions on alcohol advertising on TV would have a small negative effect on drinking, and this effect would be larger for heavy drinkers. PMID:25919364
A Behavioral Economic Model of Alcohol Advertising and Price.
Saffer, Henry; Dave, Dhaval; Grossman, Michael
2016-07-01
This paper presents a new empirical study of the effects of televised alcohol advertising and alcohol price on alcohol consumption. A novel feature of this study is that the empirical work is guided by insights from behavioral economic theory. Unlike the theory used in most prior studies, this theory predicts that restriction on alcohol advertising on TV would be more effective in reducing consumption for individuals with high consumption levels but less effective for individuals with low consumption levels. The estimation work employs data from the National Longitudinal Survey of Youth, and the empirical model is estimated with quantile regressions. The results show that advertising has a small positive effect on consumption and that this effect is relatively larger at high consumption levels. The continuing importance of alcohol taxes is also supported. Education is employed as a proxy for self-regulation, and the results are consistent with this assumption. The key conclusion is that restrictions on alcohol advertising on TV would have a small negative effect on drinking, and this effect would be larger for heavy drinkers. Copyright © 2015 John Wiley & Sons, Ltd. PMID:25919364
An EOQ Model with Two-Parameter Weibull Distribution Deterioration and Price-Dependent Demand
ERIC Educational Resources Information Center
Mukhopadhyay, Sushanta; Mukherjee, R. N.; Chaudhuri, K. S.
2005-01-01
An inventory replenishment policy is developed for a deteriorating item and price-dependent demand. The rate of deterioration is taken to be time-proportional and the time to deterioration is assumed to follow a two-parameter Weibull distribution. A power law form of the price dependence of demand is considered. The model is solved analytically…
Pricing Strategies and Models for the Provision of Digitized Texts in Higher Education.
ERIC Educational Resources Information Center
Hardy, Rachel; Oppenheim, Charles; Rubbert, Iris
2002-01-01
Describes research into charging mechanisms for the delivery of digitized texts to higher education students in the United Kingdom and discusses the need for a satisfactory pricing model. Explains the HERON (Higher Education Resources On-Demand) and PELICAN (Pricing Experiment Library Information Cooperative Network) projects and considers…
NASA Astrophysics Data System (ADS)
Zainora, A. M.; Norzailawati, M. N.; Tuminah, P.
2016-06-01
Presently, it is noticeable that there is a significant influence of public open space about house price, especially in many developed nations. Literature suggests the relationship between the two aspects give impact on the housing market, however not many studies undertaken in Malaysia. Thus, this research was initiated to analyse the relationship of open space and house price via the techniques of GIS-Hedonic Pricing Model. In this regards, the GIS tool indicates the pattern of the relationship between open space and house price spatially. Meanwhile, Hedonic Pricing Model demonstrates the index of the selected criteria in determining the housing price. This research is a perceptual study of 200 respondents who were the house owners of double-storey terrace houses in four townships, namely Bandar Baru Bangi, Taman Melawati, Subang Jaya and Shah Alam, in Klang Valley. The key research question is whether the relationship between open space and house price exists and the nature of its pattern and intensity. The findings indicate that there is a positive correlation between open space and house price. Correlation analysis reveals that a weak relationship (rs < 0.1) established between the variable of open space and house price (rs = 0.91, N = 200, p = 0.2). Consequently, the rate of house price change is rather small. In overall, this research has achieved its research aims and thus, offers the value added in applying the GIS-Hedonic pricing model in analysing the influence of open space to the house price in the form of spatially and textually.
Pricing of range accrual swap in the quantum finance Libor Market Model
NASA Astrophysics Data System (ADS)
Baaquie, Belal E.; Du, Xin; Tang, Pan; Cao, Yang
2014-05-01
We study the range accrual swap in the quantum finance formulation of the Libor Market Model (LMM). It is shown that the formulation can exactly price the path dependent instrument. An approximate price is obtained as an expansion in the volatility of Libor. The Monte Carlo simulation method is used to study the nonlinear domain of the model and determine the range of validity of the approximate formula. The price of accrual swap is analyzed by generating daily sample values by simulating a two dimension Gaussian quantum field.
Using Satellite Remote Sensing Data in a Spatially Explicit Price Model
NASA Technical Reports Server (NTRS)
Brown, Molly E.; Pinzon, Jorge E.; Prince, Stephen D.
2007-01-01
Famine early warning organizations use data from multiple disciplines to assess food insecurity of communities and regions in less-developed parts of the World. In this paper we integrate several indicators that are available to enhance the information for preparation for and responses to food security emergencies. The assessment uses a price model based on the relationship between the suitability of the growing season and market prices for coarse grain. The model is then used to create spatially continuous maps of millet prices. The model is applied to the dry central and northern areas of West Africa, using satellite-derived vegetation indices for the entire region. By coupling the model with vegetation data estimated for one to four months into the future, maps are created of a leading indicator of potential price movements. It is anticipated that these maps can be used to enable early warning of famine and for planning appropriate responses.
Lagi, Marco; Bar-Yam, Yavni; Bertrand, Karla Z; Bar-Yam, Yaneer
2015-11-10
Recent increases in basic food prices are severely affecting vulnerable populations worldwide. Proposed causes such as shortages of grain due to adverse weather, increasing meat consumption in China and India, conversion of corn to ethanol in the United States, and investor speculation on commodity markets lead to widely differing implications for policy. A lack of clarity about which factors are responsible reinforces policy inaction. Here, for the first time to our knowledge, we construct a dynamic model that quantitatively agrees with food prices. The results show that the dominant causes of price increases are investor speculation and ethanol conversion. Models that just treat supply and demand are not consistent with the actual price dynamics. The two sharp peaks in 2007/2008 and 2010/2011 are specifically due to investor speculation, whereas an underlying upward trend is due to increasing demand from ethanol conversion. The model includes investor trend following as well as shifting between commodities, equities, and bonds to take advantage of increased expected returns. Claims that speculators cannot influence grain prices are shown to be invalid by direct analysis of price-setting practices of granaries. Both causes of price increase, speculative investment and ethanol conversion, are promoted by recent regulatory changes-deregulation of the commodity markets, and policies promoting the conversion of corn to ethanol. Rapid action is needed to reduce the impacts of the price increases on global hunger. PMID:26504216
Lagi, Marco; Bar-Yam, Yavni; Bertrand, Karla Z.; Bar-Yam, Yaneer
2015-01-01
Recent increases in basic food prices are severely affecting vulnerable populations worldwide. Proposed causes such as shortages of grain due to adverse weather, increasing meat consumption in China and India, conversion of corn to ethanol in the United States, and investor speculation on commodity markets lead to widely differing implications for policy. A lack of clarity about which factors are responsible reinforces policy inaction. Here, for the first time to our knowledge, we construct a dynamic model that quantitatively agrees with food prices. The results show that the dominant causes of price increases are investor speculation and ethanol conversion. Models that just treat supply and demand are not consistent with the actual price dynamics. The two sharp peaks in 2007/2008 and 2010/2011 are specifically due to investor speculation, whereas an underlying upward trend is due to increasing demand from ethanol conversion. The model includes investor trend following as well as shifting between commodities, equities, and bonds to take advantage of increased expected returns. Claims that speculators cannot influence grain prices are shown to be invalid by direct analysis of price-setting practices of granaries. Both causes of price increase, speculative investment and ethanol conversion, are promoted by recent regulatory changes—deregulation of the commodity markets, and policies promoting the conversion of corn to ethanol. Rapid action is needed to reduce the impacts of the price increases on global hunger. PMID:26504216
2014-01-01
Gold price forecasting has been a hot issue in economics recently. In this work, wavelet neural network (WNN) combined with a novel artificial bee colony (ABC) algorithm is proposed for this gold price forecasting issue. In this improved algorithm, the conventional roulette selection strategy is discarded. Besides, the convergence statuses in a previous cycle of iteration are fully utilized as feedback messages to manipulate the searching intensity in a subsequent cycle. Experimental results confirm that this new algorithm converges faster than the conventional ABC when tested on some classical benchmark functions and is effective to improve modeling capacity of WNN regarding the gold price forecasting scheme. PMID:24744773
Li, Bai
2014-01-01
Gold price forecasting has been a hot issue in economics recently. In this work, wavelet neural network (WNN) combined with a novel artificial bee colony (ABC) algorithm is proposed for this gold price forecasting issue. In this improved algorithm, the conventional roulette selection strategy is discarded. Besides, the convergence statuses in a previous cycle of iteration are fully utilized as feedback messages to manipulate the searching intensity in a subsequent cycle. Experimental results confirm that this new algorithm converges faster than the conventional ABC when tested on some classical benchmark functions and is effective to improve modeling capacity of WNN regarding the gold price forecasting scheme. PMID:24744773
Stock price forecasting using secondary self-regression model and wavelet neural networks
NASA Astrophysics Data System (ADS)
Yang, Chi-I.; Wang, Kai-Cheng; Chang, Kuei-Fang
2015-07-01
We have established a DWT-based secondary self-regression model (AR(2)) to forecast stock value. This method requires the user to decide upon the trend of the stock prices. We later used WNN to forecast stock prices which does not require the user to decide upon the trend. When comparing these two methods, we could see that AR(2) does not perform as well if there are no trends for the stock prices. On the other hand, WNN would not be influenced by the presence of trends.
Optimization models and techniques for implementation and pricing of electricity markets
NASA Astrophysics Data System (ADS)
Madrigal Martinez, Marcelino
Vertically integrated electric power systems extensively use optimization models and solution techniques to guide their optimal operation and planning. The advent of electric power systems re-structuring has created needs for new optimization tools and the revision of the inherited ones from the vertical integration era into the market environment. This thesis presents further developments on the use of optimization models and techniques for implementation and pricing of primary electricity markets. New models, solution approaches, and price setting alternatives are proposed. Three different modeling groups are studied. The first modeling group considers simplified continuous and discrete models for power pool auctions driven by central-cost minimization. The direct solution of the dual problems, and the use of a Branch-and-Bound algorithm to solve the primal, allows to identify the effects of disequilibrium, and different price setting alternatives over the existence of multiple solutions. It is shown that particular pricing rules worsen the conflict of interest that arise when multiple solutions exist under disequilibrium. A price-setting alternative based on dual variables is shown to diminish such conflict. The second modeling group considers the unit commitment problem. An interior-point/cutting-plane method is proposed for the solution of the dual problem. The new method has better convergence characteristics and does not suffer from the parameter tuning drawback as previous methods The robustness characteristics of the interior-point/cutting-plane method, combined with a non-uniform price setting alternative, show that the conflict of interest is diminished when multiple near optimal solutions exist. The non-uniform price setting alternative is compared to a classic average pricing rule. The last modeling group concerns to a new type of linear network-constrained clearing system models for daily markets for power and spinning reserve. A new model and
Zhang, P; Husten, C; Giovino, G
2000-01-01
OBJECTIVES: This study evaluated the direct effect of the tobacco price support program on domestic cigarette consumption. METHODS: We developed an economic model of demand and supply of US tobacco to estimate how much the price support program increases the price of tobacco. We calculated the resultant increase in cigarette prices from the change in the tobacco price and the quantity of domestic tobacco contained in US cigarettes. We then assessed the reduction in cigarette consumption attributable to the price support program by applying the estimated increase in the cigarette price to assumed price elasticities of demand for cigarettes. RESULTS: We estimated that the tobacco price support program increased the price of tobacco leaf by $0.36 per pound. This higher tobacco price translates to a $0.01 increase in the price of a pack of cigarettes and an estimated 0.21% reduction in cigarette consumption. CONCLUSION: Because the tobacco price support program increases the price of cigarettes minimally, its potential health benefit is likely to be small. The adverse political effect of the tobacco program might substantially outweigh the potential direct benefit of the program on cigarette consumption. PMID:10800423
Modeling natural gas prices as a random walk: The advantages for generation planning
Felder, F.A.
1995-11-01
Random walk modeling allows decision makers to evaluate risk mitigation strategies. Easily constructed, the random walk provides probability information that long-term fuel forecasts do not. This is vital to meeting the ratepayers` need for low-cost power, the shareholders` financial objectives, and the regulators` desire for straightforward information. Power generation planning depends heavily on long-term fuel price forecasts. This is particularly true for natural gas-fired plants, because fuel expenses are a significant portion of busbar costs and are subject to considerable uncertainty. Accurate forecasts, then, are critical - especially if electric utilities are to take advantage of the current low cost of natural gas technologies and their relatively clean burning characteristics, without becoming overdependent on a fuel that might significantly increase in price. Moreover, the transition to a more competitive generation market requires a more market-driven planning process. Current planning techniques use several long-term fuel forecasts - one serving as an expected case and others for sensitivity analysis - as inputs for modeling production costs. These forecasts are deterministic: For every time interval there is one, and only one projected fuel price - a serious limitation. Further, past natural gas price predictions have been erroneous and may be susceptible to bias. Today, deregulation of the natural gas production industry allows for a new approach in long-term fuel forecasting. Using NYMEX information, a random walk model of natural gas prices can be constructed. A random walk assumes that prices move randomly, and in modeling prices in this context one would be sure to include this all-important price volatility.
Socioeconophysics:. Opinion Dynamics for Number of Transactions and Price, a Trader Based Model
NASA Astrophysics Data System (ADS)
Tuncay, Çağlar
Involving effects of media, opinion leader and other agents on the opinion of individuals of market society, a trader based model is developed and utilized to simulate price via supply and demand. Pronounced effects are considered with several weights and some personal differences between traders are taken into account. Resulting time series and probabilty distribution function involving a power law for price come out similar to the real ones.
Robust Fitting of a Weibull Model with Optional Censoring
Yang, Jingjing; Scott, David W.
2013-01-01
The Weibull family is widely used to model failure data, or lifetime data, although the classical two-parameter Weibull distribution is limited to positive data and monotone failure rate. The parameters of the Weibull model are commonly obtained by maximum likelihood estimation; however, it is well-known that this estimator is not robust when dealing with contaminated data. A new robust procedure is introduced to fit a Weibull model by using L2 distance, i.e. integrated square distance, of the Weibull probability density function. The Weibull model is augmented with a weight parameter to robustly deal with contaminated data. Results comparing a maximum likelihood estimator with an L2 estimator are given in this article, based on both simulated and real data sets. It is shown that this new L2 parametric estimation method is more robust and does a better job than maximum likelihood in the newly proposed Weibull model when data are contaminated. The same preference for L2 distance criterion and the new Weibull model also happens for right-censored data with contamination. PMID:23888090
Roberge, H.D. ); Sikora, R.P. ); Baetz, B.W. . Dept. of Civil Engineering)
1994-01-01
This note reports on a study of waste reduction options for the upstream oil and gas industry and involves the application of a waste reduction optimization model to a generic sour gas plant. The waste reduction optimization model is meant as an aid for decision-making relating to the implementation of waste reduction options. The generic facility was developed from process knowledge provided by industry members of a project steering committee, as well as waste management information from industry manuals and represents a facility of average capacity and typical configuration. Several waste minimization options were modeled for selected waste streams. The selected streams were chosen based upon waste flows and disposal costs and their potential for waste reduction. The results of the modeling for the generic sour gas plant have shown that a set of cost-effective waste reduction options exist, there is significant potential for reducing the total quantity of waste to be managed and disposed of, and that implementation of the options would lead to considerable cost savings. The value and usefulness of the modeling approach lie not only in the generated results, but also in the fact that to construct the model, relevant waste flows and every possible manner that these waste flows can be minimized or processed are systematically identified. Once modeled, the parameters can be readily manipulated to determine various possible waste management strategies. To effectively use the modeling approach, the waste reduction team should have knowledge of the plant processes, existing waste management practices and costs, information on potential waste reduction options and technologies, as well as experience in mathematical modeling and analysis.
Hill, L.J.
1994-04-01
Changing electricity prices to more closely reflect production costs has a significant impact on the consumption of electricity. It is known, for example, that most of the efficiency gains in the electric power sectors of the industrialized world since the first international oil price shock in 1973 are attributable to the rising trend of electricity prices. This was due to the rising average price of electricity. Because of the unique characteristics of producing electricity, its marginal cost is higher than its average cost during many hours of the day. This study shows that, for utilities not reflecting these cost differences in their rates, there is ample room to satisfy a portion of their resource needs by exploiting the load-shaping properties of time-of-use (TOU) rates. Satisfying a portion of resource requirements by implementing a TOU-pricing program, however, is not costless. Metering and administering TOU pricing requires a financial commitment by an electric utility. And the commitment has an opportunity cost. That is, the funds could be used to construct generating plants or run DSM programs (other than a TOU-pricing program) and satisfy the same resource needs that TOU pricing does. The question addressed in this study is whether a utility is better-served financially by (i) implementing TOU pricing or (ii) running technical DSM programs and building power plants. The answer is that TOU pricing compares favorably on a financial basis with other resources under a wide set of conditions that real-world utilities confront.
Modelling multi-pollutant compliance options for power companies
Teeth, B.; Hopkins, B.
2007-09-15
Emission control regulations in the United States require that utilities consider retrofit of reduction technologies for multiple pollutants at all plants in their fleet. Washington Group International has developed a Compliance Strategy Model that evaluates the cost of combinations of flue gas desulfurization, NOx and mercury control processes for multiple units to determine an economical mix of the control processes of the fleet of generating units in each state or designated region. The Model is based on an Excel spreadsheet which uses mixed integer routines and Premium Solver to assess up to 10{sup 40} possible combinations of emissions control processes to determine the combination with an economic present worth of revenue requirement (PWRR). Examples of use of the Model have been for consideration of NOx reduction technologies at 19 coal-fired units in one fleet and of 76 units in one fleet in five regions. 1 tab.
Adiabaticity conditions for volatility smile in Black-Scholes pricing model
NASA Astrophysics Data System (ADS)
Spadafora, L.; Berman, G. P.; Borgonovi, F.
2011-01-01
Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price C(K) given the strike price K and the distribution function of the returns. We derive this distribution function using for C(K) a Black-Scholes expression with volatility σ in the form of a volatility smile. We show that this approach based on a volatility smile leads to relative minima for the distribution function ("bad" probabilities) never observed in real data and, in the worst cases, negative probabilities. We show that these undesirable effects can be eliminated by requiring "adiabatic" conditions on the volatility smile.
A Single-Factor Model Analysis of Electricity Futures Price and its Application
NASA Astrophysics Data System (ADS)
Itoh, Yasuyuki; Kobayashi, Takenori
This paper presents a single-factor model to describe the fluctuation of the electricity futures price for its trading risk management. An autoregressive moving-average model (ARMA(2, 1) process) was used to express the stochastic process of the price, instead of a conventionally used Malkov process such as the AR(1) process, where the ARMA(2, 1) process becomes a hybrid of short- and long-term mean-reversion processes in the continuous time model. This model was applied to the analysis of the price of the electricity futures (the PJM Monthly) traded at the New York Mercantile Exchange (NYMEX). The result showed that the model well explained the term structure of the volatility of futures price with respect to the time to maturity, which is important for estimating its trading risk. The expected long-term fixed electricity price and its confidence interval were also estimated by using the obtained model function of the forward curve and its parameters.
Adapting mudharabah principle in Islamic option
NASA Astrophysics Data System (ADS)
Suhaimi, Siti Noor Aini binti; Salleh, Hassilah binti
2013-04-01
Most of the options today use the Black-Scholes model as the basis in valuing their price. This conventional model involves the elements that are strictly prohibited in Islam namely riba, gharar and maisir. Hence, this paper introduces a new mathematical model that has been adapted with mudharabah principle to replace the Black-Scholes model. This new model which is more compatible with Islamic values produces a new Islamic option which avoids any form of oppression and injustice to all parties involved.
Airborne electromagnetic modelling options and their consequences in target definition
NASA Astrophysics Data System (ADS)
Ley-Cooper, Alan Yusen; Viezzoli, Andrea; Guillemoteau, Julien; Vignoli, Giulio; Macnae, James; Cox, Leif; Munday, Tim
2015-10-01
Given the range of geological conditions under which airborne EM surveys are conducted, there is an expectation that the 2D and 3D methods used to extract models that are geologically meaningful would be favoured over 1D inversion and transforms. We do after all deal with an Earth that constantly undergoes, faulting, intrusions, and erosive processes that yield a subsurface morphology, which is, for most parts, dissimilar to a horizontal layered earth. We analyse data from a survey collected in the Musgrave province, South Australia. It is of particular interest since it has been used for mineral prospecting and for a regional hydro-geological assessment. The survey comprises abrupt lateral variations, more-subtle lateral continuous sedimentary sequences and filled palaeovalleys. As consequence, we deal with several geophysical targets of contrasting conductivities, varying geometries and at different depths. We invert the observations by using several algorithms characterised by the different dimensionality of the forward operator. Inversion of airborne EM data is known to be an ill-posed problem. We can generate a variety of models that numerically adequately fit the measured data, which makes the solution non-unique. The application of different deterministic inversion codes or transforms to the same dataset can give dissimilar results, as shown in this paper. This ambiguity suggests the choice of processes and algorithms used to interpret AEM data cannot be resolved as a matter of personal choice and preference. The degree to which models generated by a 1D algorithm replicate/or not measured data, can be an indicator of the data's dimensionality, which perse does not imply that data that can be fitted with a 1D model cannot be multidimensional. On the other hand, it is crucial that codes that can generate 2D and 3D models do reproduce the measured data in order for them to be considered as a plausible solution. In the absence of ancillary information, it could
Pricing and Enrollment Planning.
ERIC Educational Resources Information Center
Martin, Robert E.
2003-01-01
Presents a management model for pricing and enrollment planning that yields optimal pricing decisions relative to student fees and average scholarship, the institution's financial ability to support students, and an average cost-pricing rule. (SLD)
Modeling the Development of Children's Use of Optional Infinitives in Dutch and English Using MOSAIC
ERIC Educational Resources Information Center
Freudenthal, Daniel; Pine, Julian M.; Gobet, Fernand
2006-01-01
In this study we use a computational model of language learning called model of syntax acquisition in children (MOSAIC) to investigate the extent to which the optional infinitive (OI) phenomenon in Dutch and English can be explained in terms of a resource-limited distributional analysis of Dutch and English child-directed speech. The results show…
Vanderbei, Robert J.; P Latin-Small-Letter-Dotless-I nar, Mustafa C.; Bozkaya, Efe B.
2013-02-15
An American option (or, warrant) is the right, but not the obligation, to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option differs from a plain American option in that it does not expire. In this study, we solve the optimal stopping problem of a perpetual American option (both call and put) in discrete time using linear programming duality. Under the assumption that the underlying stock price follows a discrete time and discrete state Markov process, namely a geometric random walk, we formulate the pricing problem as an infinite dimensional linear programming (LP) problem using the excessive-majorant property of the value function. This formulation allows us to solve complementary slackness conditions in closed-form, revealing an optimal stopping strategy which highlights the set of stock-prices where the option should be exercised. The analysis for the call option reveals that such a critical value exists only in some cases, depending on a combination of state-transition probabilities and the economic discount factor (i.e., the prevailing interest rate) whereas it ceases to be an issue for the put.
Modeling stock price dynamics by continuum percolation system and relevant complex systems analysis
NASA Astrophysics Data System (ADS)
Xiao, Di; Wang, Jun
2012-10-01
The continuum percolation system is developed to model a random stock price process in this work. Recent empirical research has demonstrated various statistical features of stock price changes, the financial model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price, in an attempt to reproduce and explain this set of empirical facts. The continuum percolation model is usually referred to as a random coverage process or a Boolean model, the local interaction or influence among traders is constructed by the continuum percolation, and a cluster of continuum percolation is applied to define the cluster of traders sharing the same opinion about the market. We investigate and analyze the statistical behaviors of normalized returns of the price model by some analysis methods, including power-law tail distribution analysis, chaotic behavior analysis and Zipf analysis. Moreover, we consider the daily returns of Shanghai Stock Exchange Composite Index from January 1997 to July 2011, and the comparisons of return behaviors between the actual data and the simulation data are exhibited.
McIntyre, Di; Ataguba, John E
2012-03-01
South Africa is considering introducing a universal health care system. A key concern for policy-makers and the general public is whether or not this reform is affordable. Modelling the resource and revenue generation requirements of alternative reform options is critical to inform decision-making. This paper considers three reform scenarios: universal coverage funded by increased allocations to health from general tax and additional dedicated taxes; an alternative reform option of extending private health insurance coverage to all formal sector workers and their dependents with the remainder using tax-funded services; and maintaining the status quo. Each scenario was modelled over a 15-year period using a spreadsheet model. Statistical analyses were also undertaken to evaluate the impact of options on the distribution of health care financing burden and benefits from using health services across socio-economic groups. Universal coverage would result in total health care spending levels equivalent to 8.6% of gross domestic product (GDP), which is comparable to current spending levels. It is lower than the status quo option (9.5% of GDP) and far lower than the option of expanding private insurance cover (over 13% of GDP). However, public funding of health services would have to increase substantially. Despite this, universal coverage would result in the most progressive financing system if the additional public funding requirements are generated through a surcharge on taxable income (but not if VAT is increased). The extended private insurance scheme option would be the least progressive and would impose a very high payment burden; total health care payments on average would be 10.7% of household consumption expenditure compared with the universal coverage (6.7%) and status quo (7.5%) options. The least pro-rich distribution of service benefits would be achieved under universal coverage. Universal coverage is affordable and would promote health system equity, but
Modelling approach to LILW-SL repository safety evaluation for different waste packing options
Perko, Janez; Mallants, Dirk; Volckaert, Geert; Towler, George; Egan, Mike; Virsek, Sandi; Hertl, Bojan
2007-07-01
The key objective of the work described here was to support the identification of a preferred disposal concept and packaging option for low and short-lived intermediate level waste (LILW-SL). The emphasis of the assessment, conducted on behalf of the Slovenian radioactive waste management agency (ARAO), was the consideration of several waste treatment and packaging options in an attempt to identify optimised containment characteristics that would result in safe disposal, taking into account the cost-benefit of alternative safety measures. Waste streams for which alternative treatment and packaging solutions were developed and evaluated include decommissioning waste and NPP operational wastes, including drums with unconditioned ion exchange resins in over-packed tube type containers (TTCs). For decommissioning wastes, the disposal options under consideration were either direct disposal of loose pieces grouted into a vault or use of high integrity containers (HIC). In relation to operational wastes, three main options were foreseen. The first is over-packing of resin containing TTCs grouted into high integrity containers, the second option is complete treatment with hydration, neutralization, and cementation of the dry resins into drums grouted into high integrity containers and the third is direct disposal of TTCs into high integrity containers without additional treatment. The long-term safety of radioactive waste repositories is usually demonstrated with the support of a safety assessment. This normally includes modelling of radionuclide release from a multi-barrier near-surface or deep repository to the geosphere and biosphere. For the current work, performance assessment models were developed for each combination of siting option, repository design and waste packaging option. Modelling of releases from the engineered containment system (the 'near-field') was undertaken using the AMBER code. Detailed unsaturated water flow modelling was undertaken using the
Neural Models: An Option to Estimate Seismic Parameters of Accelerograms
NASA Astrophysics Data System (ADS)
Alcántara, L.; García, S.; Ovando-Shelley, E.; Macías, M. A.
2014-12-01
Seismic instrumentation for recording strong earthquakes, in Mexico, goes back to the 60´s due the activities carried out by the Institute of Engineering at Universidad Nacional Autónoma de México. However, it was after the big earthquake of September 19, 1985 (M=8.1) when the project of seismic instrumentation assumes a great importance. Currently, strong ground motion networks have been installed for monitoring seismic activity mainly along the Mexican subduction zone and in Mexico City. Nevertheless, there are other major regions and cities that can be affected by strong earthquakes and have not yet begun their seismic instrumentation program or this is still in development.Because of described situation some relevant earthquakes (e.g. Huajuapan de León Oct 24, 1980 M=7.1, Tehuacán Jun 15, 1999 M=7 and Puerto Escondido Sep 30, 1999 M= 7.5) have not been registered properly in some cities, like Puebla and Oaxaca, and that were damaged during those earthquakes. Fortunately, the good maintenance work carried out in the seismic network has permitted the recording of an important number of small events in those cities. So in this research we present a methodology based on the use of neural networks to estimate significant duration and in some cases the response spectra for those seismic events. The neural model developed predicts significant duration in terms of magnitude, epicenter distance, focal depth and soil characterization. Additionally, for response spectra we used a vector of spectral accelerations. For training the model we selected a set of accelerogram records obtained from the small events recorded in the strong motion instruments installed in the cities of Puebla and Oaxaca. The final results show that neural networks as a soft computing tool that use a multi-layer feed-forward architecture provide good estimations of the target parameters and they also have a good predictive capacity to estimate strong ground motion duration and response spectra.
An agent-based approach to modelling the effects of extreme events on global food prices
NASA Astrophysics Data System (ADS)
Schewe, Jacob; Otto, Christian; Frieler, Katja
2015-04-01
Extreme climate events such as droughts or heat waves affect agricultural production in major food producing regions and therefore can influence the price of staple foods on the world market. There is evidence that recent dramatic spikes in grain prices were at least partly triggered by actual and/or expected supply shortages. The reaction of the market to supply changes is however highly nonlinear and depends on complex and interlinked processes such as warehousing, speculation, and export restrictions. Here we present for the first time an agent-based modelling framework that accounts, in simplified terms, for these processes and allows to estimate the reaction of world food prices to supply shocks on a short (monthly) timescale. We test the basic model using observed historical supply, demand, and price data of wheat as a major food grain. Further, we illustrate how the model can be used in conjunction with biophysical crop models to assess the effect of future changes in extreme event regimes on the volatility of food prices. In particular, the explicit representation of storage dynamics makes it possible to investigate the potentially nonlinear interaction between simultaneous extreme events in different food producing regions, or between several consecutive events in the same region, which may both occur more frequently under future global warming.
Stochastic modeling of stock price process induced from the conjugate heat equation
NASA Astrophysics Data System (ADS)
Paeng, Seong-Hun
2015-02-01
Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.
Tuition Elasticity of the Demand for Higher Education among Current Students: A Pricing Model.
ERIC Educational Resources Information Center
Bryan, Glenn A.; Whipple, Thomas W.
1995-01-01
A pricing model is offered, based on retention of current students, that colleges can use to determine appropriate tuition. A computer-based model that quantifies the relationship between tuition elasticity and projected net return to the college was developed and applied to determine an appropriate tuition rate for a small, private liberal arts…
Crop Monitoring as a Tool for Modelling the Genesis of Millet Prices in Senegal
NASA Astrophysics Data System (ADS)
Jacques, D.; Marinho, E.; Defourny, P.; Waldner, F.; d'Andrimont, R.
2015-12-01
Food security in Sahelian countries strongly relies on the ability of markets to transfer staplesfrom surplus to deficit areas. Market failures, leading to the inefficient geographical allocation of food,are expected to emerge from high transportation costs and information asymmetries that are commonin moderately developed countries. As a result, important price differentials are observed betweenproducing and consuming areas which damages both poor producers and food insecure consumers. Itis then vital for policy makers to understand how the prices of agricultural commodities are formed byaccounting for the existing market imperfections in addition to local demand and supply considerations. To address this issue, we have gathered an unique and diversified set of data for Senegal andintegrated it in a spatially explicit model that simulates the functioning of agricultural markets, that isfully consistent with the economic theory. Our departure point is a local demand and supply modelaround each market having its catchment areas determined by the road network. We estimate the localsupply of agricultural commodities from satellite imagery while the demand is assumed to be a functionof the population living in the area. From this point on, profitable transactions between areas with lowprices to areas with high prices are simulated for different levels of per kilometer transportation costand information flows (derived from call details records i.e. mobile phone data). The simulated prices are then comparedwith the actual millet prices. Despite the parsimony of the model that estimates only two parameters, i.e. the per kilometertransportation cost and the information asymmetry resulting from low levels of mobile phone activitybetween markets, it impressively explains more than 80% of the price differentials observed in the 40markets included in the analysis. In one hand these results can be used in the assessment of the socialwelfare impacts of the further development of
NASA Astrophysics Data System (ADS)
Chen, Dar-Hsin; Chou, Heng-Chih; Wang, David; Zaabar, Rim
2011-06-01
Most empirical research of the path-dependent, exotic-option credit risk model focuses on developed markets. Taking Taiwan as an example, this study investigates the bankruptcy prediction performance of the path-dependent, barrier option model in the emerging market. We adopt Duan's (1994) [11], (2000) [12] transformed-data maximum likelihood estimation (MLE) method to directly estimate the unobserved model parameters, and compare the predictive ability of the barrier option model to the commonly adopted credit risk model, Merton's model. Our empirical findings show that the barrier option model is more powerful than Merton's model in predicting bankruptcy in the emerging market. Moreover, we find that the barrier option model predicts bankruptcy much better for highly-leveraged firms. Finally, our findings indicate that the prediction accuracy of the credit risk model can be improved by higher asset liquidity and greater financial transparency.