标的资产价格服从分数布朗运动的几种新型期权定价  

The Pricing Formulas of Exotic Options in a Fractional Brownian Motion

作　　者：刘海媛[1] 周圣武[1] 索新丽[1] 

机构地区：[1]中国矿业大学理学院,江苏徐州221008

出　　处：《数学的实践与认识》2008年第15期54-59,共6页Mathematics in Practice and Theory

基　　金：中国矿业大学青年科研基金(2007A029)

摘　　要：在等价鞅测度下,研究标的资产价格服从分数布朗运动的几种新型股票期权定价公式——n次幂期权、(幂型)上封顶及下保底型欧式看涨期权.并与基于标准布朗运动的期权定价公式进行比较分析,进一步论证布朗运动只是分数布朗运动的一种特例,可基于分数布朗运动对原有的期权定价模型进行推广.By applying equivalent martingale measure, the purpose of this paper is to obtain pricing formulas for some exotic options including power option, capped option, if the underlying is driven by a Fractional Brownian Motion. We will compare our results with the classical results based on standard Brownian Motion. And we conclude that standard Brownian Motion is an especial case of Fractional Brownian Motion. Then the classical pricing model of option can be generalized, which is based on Fractional Brownian Motion.

关 键 词：分数布朗运动 Black—Scholes公式 新型期权 

分 类 号：F830.91[经济管理—金融学] F224