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Volume 12, Issue 3
Fitted Finite Volume Method for Pricing American Options under Regime-Switching Jump-Diffusion Models Based on Penalty Method

Xiaoting Gan, Jun-Feng Yin & Rui Li

Adv. Appl. Math. Mech., 12 (2020), pp. 748-773.

Published online: 2020-04

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  • Abstract

In this paper we develop a novel numerical method for pricing American options under regime-switching jump-diffusion models which are governed by a system of partial integro-differential complementarity problems (PIDCPs). Based on a penalty approach, the PIDCPs results in a set of coupled nonlinear partial integro-differential equations (PIDEs). To numerically solve these nonlinear penalized PIDEs, we introduce a fitted finite volume method for the spatial discretization, coupled with the backward Euler and Crank-Nicolson time stepping schemes. We show that these schemes are consistent, stable and monotone, hence it ensures the convergence to the solution of continuous problem. To solve the discretized nonlinear system effectively, an iterative method is designed. Numerical experiments are presented to demonstrate the accuracy, efficiency and robustness of the new numerical method.

  • Keywords

American option pricing, regime-switching jump-diffusion model, complementarity problem, fitted finite volume method, Penalty method.

  • AMS Subject Headings

65M06, 65M12, 65M32, 91G60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

9xtgan@alumni.tongji.edu.cn (Xiaoting Gan)

yinjf@tongji.edu.cn (Jun-Feng Yin)

lirui@tongji.edu.cn (Rui Li)

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@Article{AAMM-12-748, author = {Xiaoting and Gan and 9xtgan@alumni.tongji.edu.cn and 7326 and School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China and Xiaoting Gan and Jun-Feng and Yin and yinjf@tongji.edu.cn and 12517 and School of Mathematical Sciences, Tongji University, Shanghai 200092, P.R. China and Jun-Feng Yin and Rui and Li and lirui@tongji.edu.cn and 13647 and School of Mathematical Sciences, Tongji University, Shanghai, 200092, China and Rui Li}, title = {Fitted Finite Volume Method for Pricing American Options under Regime-Switching Jump-Diffusion Models Based on Penalty Method}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {3}, pages = {748--773}, abstract = {

In this paper we develop a novel numerical method for pricing American options under regime-switching jump-diffusion models which are governed by a system of partial integro-differential complementarity problems (PIDCPs). Based on a penalty approach, the PIDCPs results in a set of coupled nonlinear partial integro-differential equations (PIDEs). To numerically solve these nonlinear penalized PIDEs, we introduce a fitted finite volume method for the spatial discretization, coupled with the backward Euler and Crank-Nicolson time stepping schemes. We show that these schemes are consistent, stable and monotone, hence it ensures the convergence to the solution of continuous problem. To solve the discretized nonlinear system effectively, an iterative method is designed. Numerical experiments are presented to demonstrate the accuracy, efficiency and robustness of the new numerical method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0017}, url = {http://global-sci.org/intro/article_detail/aamm/16422.html} }
TY - JOUR T1 - Fitted Finite Volume Method for Pricing American Options under Regime-Switching Jump-Diffusion Models Based on Penalty Method AU - Gan , Xiaoting AU - Yin , Jun-Feng AU - Li , Rui JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 748 EP - 773 PY - 2020 DA - 2020/04 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0017 UR - https://global-sci.org/intro/article_detail/aamm/16422.html KW - American option pricing, regime-switching jump-diffusion model, complementarity problem, fitted finite volume method, Penalty method. AB -

In this paper we develop a novel numerical method for pricing American options under regime-switching jump-diffusion models which are governed by a system of partial integro-differential complementarity problems (PIDCPs). Based on a penalty approach, the PIDCPs results in a set of coupled nonlinear partial integro-differential equations (PIDEs). To numerically solve these nonlinear penalized PIDEs, we introduce a fitted finite volume method for the spatial discretization, coupled with the backward Euler and Crank-Nicolson time stepping schemes. We show that these schemes are consistent, stable and monotone, hence it ensures the convergence to the solution of continuous problem. To solve the discretized nonlinear system effectively, an iterative method is designed. Numerical experiments are presented to demonstrate the accuracy, efficiency and robustness of the new numerical method.

Xiaoting Gan, Jun-Feng Yin & Rui Li. (2020). Fitted Finite Volume Method for Pricing American Options under Regime-Switching Jump-Diffusion Models Based on Penalty Method. Advances in Applied Mathematics and Mechanics. 12 (3). 748-773. doi:10.4208/aamm.OA-2019-0017
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