Journal of Mathematics and Statistics

An Approximate Formula of European Option for Fractional Stochastic Volatility Jump-Diffusion Model

P. Sattayatham and A. Intarasit

DOI : 10.3844/jmssp.2011.230.238

Journal of Mathematics and Statistics

Volume 7, Issue 3

Pages 230-238

Abstract

Problem statement: We presented option pricing when the stock prices follows a jumpdiffusion model and their stochastic volatility follows a fractional stochastic volatility model. This proposed model exhibits the a memory of a stochastic volatility model that is not expressed in the classical stochastic volatility model. Approach: We introduce an approximated method to fractional stochastic volatility model perturbed by the fractional Brownian motion. A relationship between stochastic differential equations and partial differential equations for a bivariate model is presented. Results: By using an approximate method, we provide the approximate solution of the fractional stochastic volatility model. And European options are priced by using the risk-neutral valuation. Conclusion/Recommendations: The formula of European option is calculated by using the technique base on the characteristic function of an underlying asset which can be expressed in an explicit formula. A numerical integration technique to simulation fractional stochastic volatility are presented in this study.

Copyright

© 2011 P. Sattayatham and A. Intarasit. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.