path integral approach to closed form pricing formulas in the Heston framework.

NASA Astrophysics Data System (ADS)

Lemmens, Damiaan; Wouters, Michiel; Tempere, Jacques; Foulon, Sven

2008-03-01

We present a path integral approach for finding closed form formulas for option prices in the framework of the Heston model. The first model for determining option prices was the Black-Scholes model, which assumed that the logreturn followed a Wiener process with a given drift and constant volatility. To provide a realistic description of the market, the Black-Scholes results must be extended to include stochastic volatility. This is achieved by the Heston model, which assumes that the volatility follows a mean reverting square root process. Current applications of the Heston model are hampered by the unavailability of fast numerical methods, due to a lack of closed-form formulae. Therefore the search for closed form solutions is an essential step before the qualitatively better stochastic volatility models will be used in practice. To attain this goal we outline a simplified path integral approach yielding straightforward results for vanilla Heston options with correlation. Extensions to barrier options and other path-dependent option are discussed, and the new derivation is compared to existing results obtained from alternative path-integral approaches (Dragulescu, Kleinert).

Multi-criteria optimization of chassis parameters of Nissan 200 SX for drifting competitions

NASA Astrophysics Data System (ADS)

Maniowski, M.

2016-09-01

The work objective is to increase performance of Nissan 200sx S13 prepared for a quasi-static state of drifting on a circular path with given constant radius (R=15 m) and tyre-road friction coefficient (μ = 0.9). First, a high fidelity “miMA” multibody model of the vehicle is formulated. Then, a multicriteria optimization problem is solved with one of the goals to maximize a stable drift angle (β) of the vehicle. The decision variables contain 11 parameters of the vehicle chassis (describing the wheel suspension stiffness and geometry) and 2 parameters responsible for a driver steering and accelerator actions, that control this extreme closed-loop manoeuvre. The optimized chassis setup results in the drift angle increase by 14% from 35 to 40 deg.

Stormtime transport of ring current and radiation belt ions

NASA Technical Reports Server (NTRS)

Chen, Margaret W.; Schulz, Michael; Lyons, L. R.; Gorney, David J.

1993-01-01

This is an investigation of stormtime particle transport that leads to formation of the ring current. Our method is to trace the guiding-center motion of representative ions (having selected first adiabatic invariants mu) in response to model substorm-associated impulses in the convection electric field. We compare our simulation results qualitatively with existing analytically tractable idealizations of particle transport (direct convective access and radial diffusion) in order to assess the limits of validity of these approximations. For mu approximately less than 10 MeV/G (E approximately less than 10 keV at L equivalent to 3) the ion drift period on the final (ring-current) drift shell of interest (L equivalent to 3) exceeds the duration of the main phase of our model storm, and we find that the transport of ions to this drift shell is appropriately idealized as direct convective access, typically from open drift paths. Ion transport to a final closed drift path from an open (plasma-sheet) drift trajectory is possible for those portions of that drift path that lie outside the mean stormtime separatrix between closed and open drift trajectories, For mu approximately 10-25 MeV/G (110 keV approximately less than E approximately less than 280 keV at L equivalent to 3) the drift period at L equivalent to 3 is comparable to the postulated 3-hr duration of the storm, and the mode of transport is transitional between direct convective access and transport that resembles radial diffusion. (This particle population is transitional between the ring current and radiation belt). For mu approximately greater than 25 MeV/G (radiation-belt ions having E approximately greater than 280 keV at L equivalent to 3) the ion drift period is considerably shorter than the main phase of a typical storm, and ions gain access to the ring-current region essentially via radial diffusion. By computing the mean and mean-square cumulative changes in 1/L among (in this case) 12 representative ions equally spaced in drift time around the steady-state drift shell of interest (L equivalent to 3), we have estimated (from both our forward and our time-reversed simulations) the time-integrated radial-diffusion coefficients D(sup sim)(sub LL) for particles having selected values of mu approximately greater than 15 MeV/G. The results agree surprisingly well with the predictions (D(sup ql)(sub LL)) of quasilinear radial diffusion theory, despite the rather brief duration (approximately 3 hrs) of our model storm and despite the extreme variability (with frequency) of the spectral-density function that characterizes the applied electric field during our model storm. As expected, the values of D(sup sim)(sub LL) deduced (respectively) from our forward and time-reversed simulations agree even better with each other and with D(sup sim)(sub LL) when the impulse amplitudes which characterize the individual substorms of our model storm are systematically reduced.

Comparison of Lyman-alpha and LI-COR infrared hygrometers for airborne measurement of turbulent fluctuations of water vapour

NASA Astrophysics Data System (ADS)

Lampert, Astrid; Hartmann, Jörg; Pätzold, Falk; Lobitz, Lennart; Hecker, Peter; Kohnert, Katrin; Larmanou, Eric; Serafimovich, Andrei; Sachs, Torsten

2018-05-01

To investigate if the LI-COR humidity sensor can be used as a replacement of the Lyman-alpha sensor for airborne applications, the measurement data of the Lyman-alpha and several LI-COR sensors are analysed in direct intercomparison flights on different airborne platforms. One vibration isolated closed-path and two non-isolated open-path LI-COR sensors were installed on a Dornier 128 twin engine turbo-prop aircraft. The closed-path sensor provided absolute values and fluctuations of the water vapour mixing ratio in good agreement with the Lyman-alpha. The signals of the two open-path sensors showed considerable high-frequency noise, and the absolute value of the mixing ratio was observed to drift with time in this vibrational environment. On the helicopter-towed sensor system Helipod, with very low vibration levels, the open-path LI-COR sensor agreed very well with the Lyman-alpha sensor over the entire frequency range up to 3 Hz. The results show that the LI-COR sensors are well suited for airborne measurements of humidity fluctuations, provided that a vibrationless environment is given, and this turns out to be more important than close sensor spacing.

Ionospheric Plasma Drift Analysis Technique Based On Ray Tracing

NASA Astrophysics Data System (ADS)

Ari, Gizem; Toker, Cenk

2016-07-01

Ionospheric drift measurements provide important information about the variability in the ionosphere, which can be used to quantify ionospheric disturbances caused by natural phenomena such as solar, geomagnetic, gravitational and seismic activities. One of the prominent ways for drift measurement depends on instrumentation based measurements, e.g. using an ionosonde. The drift estimation of an ionosonde depends on measuring the Doppler shift on the received signal, where the main cause of Doppler shift is the change in the length of the propagation path of the signal between the transmitter and the receiver. Unfortunately, ionosondes are expensive devices and their installation and maintenance require special care. Furthermore, the ionosonde network over the world or even Europe is not dense enough to obtain a global or continental drift map. In order to overcome the difficulties related to an ionosonde, we propose a technique to perform ionospheric drift estimation based on ray tracing. First, a two dimensional TEC map is constructed by using the IONOLAB-MAP tool which spatially interpolates the VTEC estimates obtained from the EUREF CORS network. Next, a three dimensional electron density profile is generated by inputting the TEC estimates to the IRI-2015 model. Eventually, a close-to-real situation electron density profile is obtained in which ray tracing can be performed. These profiles can be constructed periodically with a period of as low as 30 seconds. By processing two consequent snapshots together and calculating the propagation paths, we estimate the drift measurements over any coordinate of concern. We test our technique by comparing the results to the drift measurements taken at the DPS ionosonde at Pruhonice, Czech Republic. This study is supported by TUBITAK 115E915 and Joint TUBITAK 114E092 and AS CR14/001 projects.

A statistical study of ion pitch-angle distributions

NASA Technical Reports Server (NTRS)

Sibeck, D. G.; Mcentire, R. W.; Lui, A. T. Y.; Krimigis, S. M.

1987-01-01

Preliminary results of a statistical study of energetic (34-50 keV) ion pitch-angle distributions (PADs) within 9 Re of earth provide evidence for an orderly pattern consistent with both drift-shell splitting and magnetopause shadowing. Normal ion PADs dominate the dayside and inner magnetosphere. Butterfly PADs typically occur in a narrow belt stretching from dusk to dawn through midnight, where they approach within 6 Re of earth. While those ion butterfly PADs that typically occur on closed drift paths are mainly caused by drift-shell splitting, there is also evidence for magnetopause shadowing in observations of more frequent butterfly PAD occurrence in the outer magnetosphere near dawn than dusk. Isotropic and gradient boundary PADs terminate the tailward extent of the butterfly ion PAD belt.

Extensive electron transport and energization via multiple, localized dipolarizing flux bundles

NASA Astrophysics Data System (ADS)

Gabrielse, Christine; Angelopoulos, Vassilis; Harris, Camilla; Artemyev, Anton; Kepko, Larry; Runov, Andrei

2017-05-01

Using an analytical model of multiple dipolarizing flux bundles (DFBs) embedded in earthward traveling bursty bulk flows, we demonstrate how equatorially mirroring electrons can travel long distances and gain hundreds of keV from betatron acceleration. The model parameters are constrained by four Time History of Events and Macroscale Interactions during Substorms satellite observations, putting limits on the DFBs' speed, location, and magnetic and electric field magnitudes. We find that the sharp, localized peaks in magnetic field have such strong spatial gradients that energetic electrons ∇B drift in closed paths around the peaks as those peaks travel earthward. This is understood in terms of the third adiabatic invariant, which remains constant when the field changes on timescales longer than the electron's drift timescale: An energetic electron encircles a sharp peak in magnetic field in a closed path subtending an area of approximately constant flux. As the flux bundle magnetic field increases the electron's drift path area shrinks and the electron is prevented from escaping to the ambient plasma sheet, while it continues to gain energy via betatron acceleration. When the flux bundles arrive at and merge with the inner magnetosphere, where the background field is strong, the electrons suddenly gain access to previously closed drift paths around the Earth. DFBs are therefore instrumental in transporting and energizing energetic electrons over long distances along the magnetotail, bringing them to the inner magnetosphere and energizing them by hundreds of keV.