模糊环境中跳扩散模型下带交易费用的期权定价方法

数学物理学报 ›› 2015, Vol. 35 ›› Issue (1): 118-130.

模糊环境中跳扩散模型下带交易费用的期权定价方法

肖爽¹, 蹇明², 陈爱香², 蹇贝³

1. 华中科技大学管理学院武汉 430074 2. 华中科技大学数学与统计学院武汉 430074 3. 华中科技大学软件学院武汉 430074

收稿日期:2013-08-14 修回日期:2014-11-17 出版日期:2015-02-25 发布日期:2015-02-25

Fuzzy Pricing Formula for European Options with Jumps and Transaction Costs

XIAO Shuang¹, JIAN Ming², CHEN Ai-Xiang², JIAN Bei³

1. Management School, Huazhong University of Science and Technology, Wuhan 430074 2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074 3. School of Software, Huazhong University of Science and Technology, Wuhan 430074

Received:2013-08-14 Revised:2014-11-17 Online:2015-02-25 Published:2015-02-25

摘要/Abstract

摘要：

不确定性是金融市场的一大特性, 许多金融数据不能用确定的数来表示, 例如人们经常运用市场无风险利率为5%左右, 波动率3%左右等等这些具有模糊性的数据, 为了描述这些数据, 模糊数学被引入到金融理论中.该文将在标的资产服从Merton跳扩散过程的基础上, 考虑模糊环境中带有交易费用的期权定价问题.首先, 推导出跳扩散模型下带有交易费用的欧式看涨期权的定价公式.然后, 将模糊理论引入到期权定价中, 得到模糊环境中跳扩散模型下带交易费用的期权定价公式, 再利用模糊积分进行退模糊化.最后, 运用Sage软件对模型进行数值分析, 并与已有模型进行比较.

关键词: 跳扩散 , 交易费用 , 模糊 , 期权定价.

Abstract:

In this paper, we consider the fuzzy pricing problems for European options with jumps and transaction costs, based on the Merton's jump diffusion model. First, we deduce the pricing formula for European call options with jumps and transactions,and then the fuzzy counterpart of it is given by applying the fuzzy mathematical theory. Also, we provid the disfuzzification method for the obtained European call option pricing formula with the help of fuzzy integration. In the end, some illustrative numerical analysis examples are executed with Sage codes.

Key words: Jump diffusion , Transaction costs , Fuzzy , Option pricing.

中图分类号:

00A99

肖爽, 蹇明, 陈爱香, 蹇贝. 模糊环境中跳扩散模型下带交易费用的期权定价方法[J]. 数学物理学报, 2015, 35(1): 118-130.

XIAO Shuang, JIAN Ming, CHEN Ai-Xiang, JIAN Bei. Fuzzy Pricing Formula for European Options with Jumps and Transaction Costs[J]. Acta mathematica scientia,Series A, 2015, 35(1): 118-130.

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