混合分数布朗运动下的回望期权定价

doi:10.3969/j.issn.1000-5641.2018.04.005

华东师范大学学报(自然科学版) ›› 2018, Vol. 2018 ›› Issue (4): 47-58.doi: 10.3969/j.issn.1000-5641.2018.04.005

混合分数布朗运动下的回望期权定价

陈海珍, 周圣武, 孙祥艳

中国矿业大学数学系, 江苏徐州 221116

收稿日期:2017-07-10 出版日期:2018-07-25 发布日期:2018-07-19
通讯作者: 周圣武,男,教授,硕士生导师,研究方向为金融衍生产品的定价、统计学等.E-mail:zswcumt@163.com E-mail:zswcumt@163.com
作者简介:陈海珍,女,硕士研究生,研究方向为金融衍生产品的定价.E-mail:15269085316@163.com
基金资助:
国家自然科学基金（61304088）

Pricing of lookback options under a mixed fractional Brownian movement

CHEN Hai-zhen, ZHOU Sheng-wu, SUN Xiang-yan

Department of Mathematics, China University of Mining and Technology, Xuzhou Jiangsu 221116, China

Received:2017-07-10 Online:2018-07-25 Published:2018-07-19

摘要/Abstract

摘要： 文章主要研究了当标的股票价格由混合分数布朗运动驱动，且支付固定交易费用时欧式回望看跌期权的定价问题.首先运用对冲原理得到该模型下欧式回望看跌期权价值所满足的非线性偏微分方程及其边界条件.然后通过变量替换将得到的偏微分方程进行降维.之后又通过对变换后的新方程构造Crank-Nicolson格式来求其数值解.最后讨论了该数值格式的收敛性、交易费比率、Hurst指数等对期权价值的影响.

关键词: 混合分数布朗运动, 交易费, 欧式回望期权, Crank-Nicolson格式

Abstract: This paper studied the pricing of European lookback options when the underlying asset followed a mixed fractional Brownian movement and the transaction costs were considered. Firstly, the nonlinear partial differential equation and its boundary condition were obtained using the hedging principle under the model. Secondly, the partial differential equation was reduced using variable substitution. Next, we found its numerical solution by constructing a Crank-Nicolson format. Lastly, the convergence of the numerical scheme was discussed. We also discussed the influence of the transaction fee ratio, Hurst index, and so on.

Key words: mixed fractional Brownian movement, transaction fee, European lookback option, Crank-Nicolson format

中图分类号:

O211.6

陈海珍, 周圣武, 孙祥艳. 混合分数布朗运动下的回望期权定价[J]. 华东师范大学学报(自然科学版), 2018, 2018(4): 47-58.

CHEN Hai-zhen, ZHOU Sheng-wu, SUN Xiang-yan. Pricing of lookback options under a mixed fractional Brownian movement[J]. Journal of East China Normal University(Natural Sc, 2018, 2018(4): 47-58.

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混合分数布朗运动下的回望期权定价

Pricing of lookback options under a mixed fractional Brownian movement

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