[1]田朝薇,李锦成,翁智峰.欧式看跌期权定价问题的紧致有限差分格式[J].华侨大学学报(自然科学版),2019,40(6):830-836.[doi:10.11830/ISSN.1000-5013.201811066]
　TIAN Zhaowei,LI Jincheng,WENG Zhifeng.Compact Finite Difference Scheme for Pricing European Put Options[J].Journal of Huaqiao University(Natural Science),2019,40(6):830-836.[doi:10.11830/ISSN.1000-5013.201811066]
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欧式看跌期权定价问题的紧致有限差分格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第40卷
期数:
2019年第6期
页码:
830-836
栏目:
出版日期:
2019-11-20

文章信息/Info

Title:
Compact Finite Difference Scheme for Pricing European Put Options
文章编号:
1000-5013(2019)06-0830-07
作者:
田朝薇;  李锦成;  翁智峰
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
TIAN Zhaowei;  LI Jincheng;  WENG Zhifeng
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
Black-Scholes方程;  欧式看跌期权;  指数变换;  紧致差分格式
Keywords:
Black-Scholes equation;  European put option;  exponential transformation;  compact difference scheme
分类号:
O241;O242
DOI:
10.11830/ISSN.1000-5013.201811066
文献标志码:
A
摘要:
针对单个的Black-Scholes方程,提出一种紧致差分格式.首先,利用指数变换消去方程中的空间一阶导数;接着,在时间方向上采用CN格式,空间二阶导数采用四阶Padé逼近,构造精度为O(Δt2+h4)的紧致差分格式;然后,利用一种较为不同的离散能量法分析差分格式的稳定性和收敛性;最后,通过数值算例验证理论分析的有效性.
Abstract:
For a single Black-Scholes equation, we propose a compact difference scheme. Firstly, the first-order spatial derivative in the equation is eliminated by exponential transformation, and then a compact difference scheme with the order O(Δt2+h4)is obtained by using CN scheme for time derivative and the fourth-order Padé approximation for the second-order spatial derivatives. The stability and convergence of the difference scheme are analyzed by a different discrete energy method. Numerical examples demonstrate that the difference scheme is effective.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: 2018-11-12
通信作者: 翁智峰(1985-),男,讲师,博士,主要从事偏微分方程数值计算的研究.E-mail:zfwmath@163.com.
基金项目: 国家自然科学基金资助项目(11701197); 福建省中青年教师教育科研项目(JAT160024); 华侨大学中青年教师科研提升资助计划项目(ZQNYX502)
更新日期/Last Update: 2019-11-20