Fractional Diffusion Models of European Option with Poisson Process

Under the hypothesis of underlying asset price with long-range correlations and jump in short time, the stock price model is constructed driven by fractional Brownian motion and jump process. Then an analytic solution for European option is obtained by quasi-martingale method in the environment of fractional Brownian motion and Poisson process. For the sake of understanding the model, the influence of Hurst parameter and Poisson process are also analyzed. Finally, the model pricing efficiency is compared with Black-Scholes model and Double exponential jump diffusion option pricing model by Baotou Steel JTB1 warrants.