摘要
股价运动分形特征的发现,说明布朗运动作为期权定价模型的初始假定存在缺陷.本文假定标的资产价格服从几何分数布朗运动,利用分数风险中性测度下的拟鞅(quasi-martingale)定价方法重新求解分数Black-Scholes模型,进而对幂型期权进行定价.结果表明,幂型期权结果包含了Black-Scholes公式和平方期权结果,且相比标准期权价格,分数期权价格要同时取决于到期日和Hurst参数H.
Brownian motion is the basic hypothesis of option pricing model, which was questioned the fractal property of stock price. Given the price of assert following geometric FBM, and using of quasi-martingale method based on fractional risk neutra/measure, this paper solved fractional Black-Scholes model and European Options with Power Payoff. The result generalizes the Black-Scholes and square option formulas. And it shows fractional option price, compared to classical option price, depends on maturity time and Hurst parameter H.
出处
《经济数学》
2008年第4期356-361,共6页
Journal of Quantitative Economics
关键词
分数布朗运动
拟鞅定价
分数Black-Scholes模型
幂型期权
Fractional Brownian motion, quasi-martingale pricing, fractional Black-Scholes model, European options with power payoff
