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

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.