• 论文 •

### 状态转换下欧式Merton跳扩散期权定价的拟合有限体积方法

1. 1. 楚雄师范学院 数学与计算机科学学院, 楚雄 675000;
2. 电子科技大学 数学科学学院, 成都 611731
• 收稿日期:2019-08-16 出版日期:2021-08-15 发布日期:2021-08-20
• 基金资助:
国家自然科学基金（61463002），云南省地方本科高校（部分）基础研究联合专项面上项目（2019FH001-079）和云南省教育厅科学基金项目（2019J0369）资助.

Gan Xiaoting. FITTED FINITE VOLUME METHOD FOR PRICING EUROPEAN OPTIONS UNDER REGIME-SWITHCHING MERTON'S JUMP-DIFFUSION PROCESSES[J]. Mathematica Numerica Sinica, 2021, 43(3): 337-353.

### FITTED FINITE VOLUME METHOD FOR PRICING EUROPEAN OPTIONS UNDER REGIME-SWITHCHING MERTON'S JUMP-DIFFUSION PROCESSES

Gan Xiaoting1,2

1. 1. School of Mathematics and Computer Science, Chuxiong Normal University, Chuxiong 675000, China;
2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
• Received:2019-08-16 Online:2021-08-15 Published:2021-08-20

In this paper, a fitted finite volume method for pricing European options under regime-switching Merton's jump-diffusion model is studied. For the partial integro-differential equations (PIDEs) of this pricing model, we develop a fitted finite volume method for the spatial discretization, coupled with the Crank-Nicolson time stepping scheme. Theoretical analyses have shown that the numerical scheme is consistent, stable and monotone, hence it ensures the convergence to the solution of continuous problem. Numerical experiments are presented to verify the robustness, effectiveness and convergence of the new method.

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