摘要
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。
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.
出处
《天津商业大学学报》
2009年第4期33-37,共5页
Journal of Tianjin University of Commerce
