几何分形Brown运动的外汇期权定价

An Actuarial Approach to Foreign Currency Option Pricing

在传统期权定价中,一般考虑股票价格遵循几何Brown运动,但实际上几何Brown运动并不是刻画股票价格过程的理想工具.在实证研究中发现股票价格运动具有自相似性、长期相依性等特性,而这些特性又是几何分形Brown运动所具备的,这使得几何分形Brown运动比几何Brown运动更能准确刻画股票价格波动规律,因此讨论了遵循几何分形Brown运动时的期权定价问题,并假设利率为常数情况下,利用保险精算原理和价格过程的实际概率测度,得到了欧式外汇看涨和看跌期权的定价公式.

With the self similarity and long rang dependence, fractional Brownian motion can depict the process of stock price better then Brownian motion. Using physical probabilistic measure of price process and the principle of fair premium, this paper deals with pricing formula of option on Foreign currency option under the assumption that foreign option price process driven by fractional Brownian motion process and the fair premium principle and obtains the pricing formula of foreign option.