分数金融市场中的下出局买权定价研究

布朗运动作为Black—Scholes模型的初始假定，一直受到金融异象的质疑。分数布朗运动虽然对此进行了补救，却因本质上不是半鞅给随机计算带来困难。本文假定标的资产价格服从几何分数布朗运动，利用风险中性测度下的拟鞅（quasi—martingale）定价方法解出了分数Black—Scholes公式，最后在分数布朗运动环境中对下出局买权进行了定价。结果表明，与标准期权价格相比，分数期权价格要同时取决于到期日和Hurst参数H。

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

Brownian motion, as the basic hypothesis of Blaek-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-Seholes 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.