中文摘要：

本文研究了混合分数布朗运动环境下欧式期权定价问题.运用混合分数布朗运动的Ito公式,得到了Black-Scholes偏微分方程.同时,通过求解Black-Scholes方程,得到了欧式看涨、看跌期权的定价公式。推广了Black-Scholes模型有关欧式期权定价的结论.

英文摘要：

In this paper,the option pricing problem of European option is studied in the mixed fractional Brownian motion environment.By using fractional Ito formula,the Black-Scholes partial differential equation is obtained.And the pricing formulae of the European call and put option are obtained by partial differential equation theory.The results of Black-Scholes model are generalized.