关键词: 分数布朗运动, 分数O-U过程, 拟鞅

Abstract: Considering the time variability of stock return and long memory of volatility,afradional O-U process is given.Under the fractional risk neutral measure,we get the unique equivalent measure by using fractional Girsanov theorem.With quasi-martingale method,this paper solves an option pricing model in the fractional market,which makes original Black-Scholes equation as an special example.At last,a numerical case is employed to show that the long memory parameter H is an important factor in option pricmg.

Key words: fractional Brownian motion, fradio nal O-U process, quasi-martingale