混合分数布朗运动环境下欧式障碍期权定价

Pricing European Barrier Option in the Mixed Fractional Brownian Motion Environment

当股票价格遵循混合分数布朗运动时,利用Δ-对冲和混合分数It8公式,建立混合分数布朗运动下欧式障碍期权定价模型,通过换元法将期权定价的偏微分方程转化为热传导方程,求得显示解.在此基础上,得到欧式障碍期权看涨-看跌平价关系式.由此,再根据敲入-敲出障碍期权关系式可推出障碍期权所有类型的定价公式.

When the stock price follows the mixed fractional Brownian motion,the pricing model of European barrier option is built through the△-hedging and the mixed fractional Brownian motion Ito formulas.The partial differential equation of the European barrier call option price and its boundary condition are transformed into the heat equation by changing element,and the display solution is solved.On this basis,the European barrier option bullish-bearish parity formula can also be ob-tained.Thus,the pricing formula of all types of barrier options can be introduced according to the relationship between the bar-rier options out and in.