分数布朗运动环境中最值期权定价

Pricing of Maximum or Minimum Option in the Fractional Brownian Motion Environment

假定股票价格遵循由分数布朗运动驱动的随机微分方程,建立了分数布朗运动环境下金融市场数学模型,利用分数布朗运动随机分析理论与未定权益定价方法,获得欧式未定权益一般定价公式,并得到欧式最值期权价格的解析表达式以及平价关系。

Assuming that the stock price obeys the stochastic differential equation driven by fractional Brownian motion, we establish the mathematical model for the financial market in fractional Brownian motion setting. Using the fractional Brownian motion theory and the contingent claim pricing method,we obtain the general pricing formula for the European contingent claim. At the same time, we get the explicit expression for the European Maximum or Minimum option price and the call-put parity.