Volume 10, Issue 3
Pricing American Options under Regime-Switching Model with a Crank-Nicolson Fitted Finite Volume Method

Xiaoting Gan & Junfeng Yin

East Asian J. Appl. Math., 10 (2020), pp. 499-519.

Published online: 2020-06

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  • Abstract

A new numerical method for pricing American options under regime-switching model is developed. The original problem is first approximated by a set of nonlinear partial differential equations. After that a novel fitted finite volume method for the spatial discretisation of the nonlinear penalised system of partial differential equations is coupled with the Crank-Nicolson time stepping scheme. It is shown that the discretisation scheme is consistent, stable, monotone and hence convergent. In order to solve nonlinear algebraic systems, we apply an iterative algorithm and show its convergence. Numerical experiments demonstrate the convergence, efficiency and robustness of the numerical method.

  • Keywords

American option pricing, regime switching, fitted finite volume method, Crank-Nicolson scheme.

  • AMS Subject Headings

65M06, 65M12, 65M32, 91G60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-10-499, author = {Xiaoting Gan , and Junfeng Yin , }, title = {Pricing American Options under Regime-Switching Model with a Crank-Nicolson Fitted Finite Volume Method}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {10}, number = {3}, pages = {499--519}, abstract = {

A new numerical method for pricing American options under regime-switching model is developed. The original problem is first approximated by a set of nonlinear partial differential equations. After that a novel fitted finite volume method for the spatial discretisation of the nonlinear penalised system of partial differential equations is coupled with the Crank-Nicolson time stepping scheme. It is shown that the discretisation scheme is consistent, stable, monotone and hence convergent. In order to solve nonlinear algebraic systems, we apply an iterative algorithm and show its convergence. Numerical experiments demonstrate the convergence, efficiency and robustness of the numerical method.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.170919.221219}, url = {http://global-sci.org/intro/article_detail/eajam/16979.html} }
TY - JOUR T1 - Pricing American Options under Regime-Switching Model with a Crank-Nicolson Fitted Finite Volume Method AU - Xiaoting Gan , AU - Junfeng Yin , JO - East Asian Journal on Applied Mathematics VL - 3 SP - 499 EP - 519 PY - 2020 DA - 2020/06 SN - 10 DO - http://dor.org/10.4208/eajam.170919.221219 UR - https://global-sci.org/intro/article_detail/eajam/16979.html KW - American option pricing, regime switching, fitted finite volume method, Crank-Nicolson scheme. AB -

A new numerical method for pricing American options under regime-switching model is developed. The original problem is first approximated by a set of nonlinear partial differential equations. After that a novel fitted finite volume method for the spatial discretisation of the nonlinear penalised system of partial differential equations is coupled with the Crank-Nicolson time stepping scheme. It is shown that the discretisation scheme is consistent, stable, monotone and hence convergent. In order to solve nonlinear algebraic systems, we apply an iterative algorithm and show its convergence. Numerical experiments demonstrate the convergence, efficiency and robustness of the numerical method.

Xiaoting Gan & Junfeng Yin. (2020). Pricing American Options under Regime-Switching Model with a Crank-Nicolson Fitted Finite Volume Method. East Asian Journal on Applied Mathematics. 10 (3). 499-519. doi:10.4208/eajam.170919.221219
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