Fractional Diffusion Models of Option Prices in Markets with Jumps
Most of the recent literature dealing with the modeling of financial assets assumes that the underlying dynamics of equity prices follow a jump process or a Levy process. This is done to incorporate rare or extreme events not captured by Gaussian models. Of those financial models proposed, the most interesting include the CGMY, KoBoL and FMLS. All of these capture some of the most important characteristics of the dynamics of stock prices. In this article we show that for these particular Levy processes, the prices of financial derivatives, such as European-style options, satisfy a fractional partial differential equation (FPDE). As an application, we use numerical techniques to price exotic options, in particular barrier options, by solving the corresponding FPDEs derived.
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- Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004.
"Fractional calculus and continuous-time finance,"
- Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
- Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
- Peter Carr & Liuren Wu, 2003.
"The Finite Moment Log Stable Process and Option Pricing,"
Journal of Finance,
American Finance Association, vol. 58(2), pages 753-778, 04.
- Peter Carr & Liuren Wu, 2002. "The Finite Moment Log Stable Process and Option Pricing," Finance 0207012, EconWPA.
- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2004.
"Fractional calculus and continuous-time finance II: the waiting- time distribution,"
- Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
- Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Papers cond-mat/0006454, arXiv.org, revised Nov 2000.
- Alvaro Cartea, 2005. "Dynamic Hedging of Financial Instruments When the Underlying Follows a Non-Gaussian Process," Birkbeck Working Papers in Economics and Finance 0508, Birkbeck, Department of Economics, Mathematics & Statistics.
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