美式Kou型跳扩散期权模型的Crank-Nicolson拟合有限体积法

吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (3): 531-542.

美式Kou型跳扩散期权模型的Crank-Nicolson拟合有限体积法

江忠东, 甘小艇

楚雄师范学院数学与计算机科学学院, 云南楚雄 675000

收稿日期:2021-10-10 出版日期:2022-05-26 发布日期:2022-05-26
通讯作者: 甘小艇 E-mail:9xtgan@alumni.tongji.edu.cn

Crank-Nicolson Fitted Finite Volume Method for American Options under Kou’s Jump-Diffusion Models

JIANG Zhongdong, GAN Xiaoting

School of Mathematics and Computer Science, Chuxiong Normal University, Chuxiong 675000, Yunnan Province, China

Received:2021-10-10 Online:2022-05-26 Published:2022-05-26

摘要/Abstract

摘要： 首先, 考虑一种求解美式Kou型跳扩散期权模型的Crank-Nicolson拟合有限体积方法, 并给出收敛性分析; 其次, 针对非线性代数系统设计一个迭代算法, 并证明其收敛性；最后，用数值实验验证了新方法的收敛性、稳健性和有效性.

关键词: 美式Kou型跳扩散期权, Crank-Nicolson拟合有限体积法, 收敛性分析

Abstract: Firstly, we considered a Crank-Nicolson fitted finite volume method for solving American options under Kou’s jump-diffusion models, and gave the convergence analysis. Secondly, an iterative algorithm for the nonlinear algebraic system was designed and its convergence was proved. Finally, the convergence, robustness and effectiveness of the new method are verified by numerical experiments.

Key words: American options under Kou’s jump-diffusion model, Crank-Nicolson fitted finite volume method, convergence analysis

中图分类号:

O241.82

江忠东, 甘小艇. 美式Kou型跳扩散期权模型的Crank-Nicolson拟合有限体积法[J]. 吉林大学学报(理学版), 2022, 60(3): 531-542.

JIANG Zhongdong, GAN Xiaoting. Crank-Nicolson Fitted Finite Volume Method for American Options under Kou’s Jump-Diffusion Models[J]. Journal of Jilin University Science Edition, 2022, 60(3): 531-542.