Option Pricing in Jump-Diffusion Models with Stochastic Volatility

Many underlying assets of option contracts exhibit both jump-diffusion process and stochastic volatility. This paper investigates the valuation of options when the underlying asset follows a jump-diffusion process with stochastic volatility ,which correlated asset return process. A closed form solution is derived for European options through the use of characteristic function and the Fourier transform. The proposed model allows the option pricing formula to capture the market implied volatility smile within a unified framework.