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

Journal of Mathematics and Statistics

A. Intarasit¹  P. Sattayatham¹ 

关键词: Fractional Brownian motion;    approximate method;    fractional stochastic volatility;    jump diffusion model;    option pricing model;   

DOI  :  10.3844/jmssp.2011.230.238

学科分类：社会科学、人文和艺术（综合）

来源: Science Publications

【 摘 要 】

Problem statement: We presented option pricing when the stock prices follows a jumpdiffusionmodel and their stochastic volatility follows a fractional stochastic volatility model. Thisproposed model exhibits the a memory of a stochastic volatility model that is not expressed in theclassical stochastic volatility model. Approach: We introduce an approximated method to fractionalstochastic volatility model perturbed by the fractional Brownian motion. A relationship betweenstochastic 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 fractionalstochastic 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 techniquebase on the characteristic function of an underlying asset which can be expressed in an explicitformula. A numerical integration technique to simulation fractional stochastic volatility are presentedin this study.

【 授权许可】

Unknown