| 模糊集理论在随机波动率期权定价中的应用 |
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| 引用本文： | 李华,吴振芬.模糊集理论在随机波动率期权定价中的应用[J].数学的实践与认识,2011,41(3). |
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| 作者姓名： | 李华 吴振芬 |
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| 作者单位： | 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 |
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| 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.
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| 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 |
Application of Fuzzy Sets Theory for Option Pricing with Stochastic Volatility |
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| LI Hua,WU Zhen-fen.Application of Fuzzy Sets Theory for Option Pricing with Stochastic Volatility[J].Mathematics in Practice and Theory,2011,41(3). |
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| Authors: | LI Hua WU Zhen-fen |
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| Institution: | LI Hua~1,WU Zhen-fen~2 (1.Zhengzhou University,Department of Mathematics,Zhengzhou 450002,China) 2.Hebi College of Vocation and Technology,Department of Electorical Engeering,Hebi 458030,China) |
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| Abstract: | 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. |
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| Keywords: | European option stochastic volatility fuzzy sets possibility nonlinear PDE |
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