Research on Option Pricing Model Driven by Fractional Jump-Diffusion Process

Considering long memory of volatility of stock return and possibility of important information, this paper explores into the fractional jump-diffusion process. Under the fractional risk neutral measure, the unique equivalent measure is proposed on the basis of Girsanov fractional theorem. With quasi-martingale method, the option pricing model in fractional market is solved. The results indicate that the long memory parameter is an important factor in option pricing.