股票价格遵循分数Ornstein-Uhlenback过程的期权定价模型

Model of Option Pricing Driven by Fractional Ornstein-Uhlenback Process

本文从股价收益的时变性和波动的长记忆性两个方面考虑,建立了分数O-U过程;接着在分数风险中性测度下,利用分数情形下的Girsanov定理获得了分数O-U过程的唯一等价测度;进而采用拟鞅(quasi-martingale)定价方法,得到了分数市场环境中的期权定价模型,使得布朗运动和O-U过程驱动的期权定价模型均成为其特例;最后用算例,验证了长记忆参数H是期权定价中不可忽略的因素。

Considering the time variability of stock return and long memory of volatility, a fractional O-U process is given. Under the fractional risk neutral measure, we get the unique equivalent measure by using fractional Girsanov theorem. With quasi-martingale method, this paper solves an option pricing model in the fractional market, which makes original Black-Scholes equation as an special example. At last, a numerical case is employed to show that the long memory parameter H is an important factor in option pricing.