模糊集理论在随机波动率期权定价中的应用  

Application of Fuzzy Sets Theory for Option Pricing with Stochastic Volatility

作　　者：李华[1] 吴振芬[2] 

机构地区：[1]郑州大学数学系,河南郑州450002 [2]鹤壁职业技术学院电子信息工程系,河南鹤壁458030

出　　处：《数学的实践与认识》2011年第3期129-134,共6页Mathematics in Practice and Theory

基　　金：郑州大学人才引进项目

摘　　要：目的是对基于随机波动率模型的期权定价问题应用模糊集理论.主要思想是把波动率的概率表示转换为可能性表示,从而把关于股票价格的带随机波动率的随机过程简化为带模糊参数的随机过程.然后建立非线性偏微分方程对欧式期权进行定价.The aim of this paper is to price European options for underlying assets with stochastic volatility （SV） in Heston model in 1993 using fuzzy set theory. The main idea is to transform the probability distribution of stochastic volatility to its possibility distribution and reduce the problem to a fuzzy stochastic process for underlying asset with a new SV as a fuzzy number associated with initial SV. We use then non-linear fuzzy PDE approach to price European options.

关 键 词：欧式期权 随机波动率 模糊集 可能性理论 非线性偏微分方程 

分 类 号：O159[理学—数学] O211.6[理学—基础数学]