有限体积法定价带随机波动率的欧式期权

吉林大学学报(理学版)

有限体积法定价带随机波动率的欧式期权

甘小艇^1,2, 关南星¹, 张坤¹

1. 楚雄师范学院数学与统计学院, 云南楚雄 675000; 2. 同济大学数学系, 上海 200092

收稿日期:2016-01-11 出版日期:2016-11-26 发布日期:2016-11-29
通讯作者: 张坤 E-mail:zhangkun@cxtc.edu.cn

Finite Volume Method for Pricing European Optionswith Stochastic Volatility

GAN Xiaoting^1,2, GUAN Nanxing¹, ZHANG Kun¹

1. School of Mathematics and Statistics, Chuxiong Normal University, Chuxiong 675000, Yunnan Province,China; 2. Department of Mathematics, Tongji University, Shanghai 200092, China

Received:2016-01-11 Online:2016-11-26 Published:2016-11-29
Contact: ZHANG Kun E-mail:zhangkun@cxtc.edu.cn

摘要/Abstract

摘要： 考虑求解带随机波动率的欧式期权定价问题的有限体积方法, 先将相应的Black-Scholes方程简化为与之等价的守恒形式, 再基于重心对偶剖分和线性有限元空间, 构造向后Euler和Crank-Nicolson有限体积格式. 数值实验表明, 所构造的有限体积格式有效.

关键词: 数值实验, 有限体积法, 欧式期权定价

Abstract: We considered a finite volume method for pricing European options with stochastic volatility. We first simplified the corresponding BlackScholes equation to the equivalent conservation form. Then, we constructed backward Euler and CrankNicolson finite volume schemes based on barycenter dual partition and a linear finite element space. Numerical experiments show that the proposed finite volume schemes are effective.

Key words: finite volume method, numerical experiment, European options pricing

中图分类号:

O241.82

甘小艇, 关南星, 张坤. 有限体积法定价带随机波动率的欧式期权[J]. 吉林大学学报(理学版), 2016, 54(06): 1307-1313.

GAN Xiaoting, GUAN Nanxing, ZHANG Kun. Finite Volume Method for Pricing European Optionswith Stochastic Volatility[J]. Journal of Jilin University Science Edition, 2016, 54(06): 1307-1313.

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