On Down-and-out Call Option Pricing in Fractional Financial Market

Brownian motion,as the basic hypothesis of Black-Scholes Model,has been questioned by financial heteromorphism.Fractional Brownian motion could modify it,but that produced the difficulties in stochastic computation for it was not a semi-martingale.The paper assumes that price of assets is subject to fractional Brownian motion.Based on risk neutral measure,the paper solves fractional Black-Scholes equation and gives the down-and-out call option pricing in a fractional Brownian motion environment by the method of quasi-martingale pricing.The results show that,compared with standard option price,fractional option price depends on the maturity time and Hurst parameter H.