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Volume 15, Issue 5
On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options Under Regime-Switching Kou’s Jump-Diffusion Models

Xiaoting Gan, Junfeng Yin & Rui Li

Adv. Appl. Math. Mech., 15 (2023), pp. 1290-1314.

Published online: 2023-06

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  • Abstract

In this paper, we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou's jump-diffusion model which is governed by a system of partial integro-differential equations (PIDEs). We show that this scheme is consistent, stable and monotone as the mesh sizes in space and time approach zero, hence it ensures the convergence to the solution of continuous problem. Finally, numerical experiments are performed to demonstrate the efficiency, accuracy and robustness of the proposed method.

  • AMS Subject Headings

65M08, 65M12, 65M60, 91G60

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COPYRIGHT: © Global Science Press

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@Article{AAMM-15-1290, author = {Gan , XiaotingYin , Junfeng and Li , Rui}, title = {On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options Under Regime-Switching Kou’s Jump-Diffusion Models}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2023}, volume = {15}, number = {5}, pages = {1290--1314}, abstract = {

In this paper, we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou's jump-diffusion model which is governed by a system of partial integro-differential equations (PIDEs). We show that this scheme is consistent, stable and monotone as the mesh sizes in space and time approach zero, hence it ensures the convergence to the solution of continuous problem. Finally, numerical experiments are performed to demonstrate the efficiency, accuracy and robustness of the proposed method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2021-0016}, url = {http://global-sci.org/intro/article_detail/aamm/21777.html} }
TY - JOUR T1 - On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options Under Regime-Switching Kou’s Jump-Diffusion Models AU - Gan , Xiaoting AU - Yin , Junfeng AU - Li , Rui JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1290 EP - 1314 PY - 2023 DA - 2023/06 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2021-0016 UR - https://global-sci.org/intro/article_detail/aamm/21777.html KW - European option pricing, regime-switching Kou’s jump-diffusion model, partial integro-differential equation, fitted finite volume method, Crank-Nicolson scheme. AB -

In this paper, we construct and analyze a Crank-Nicolson fitted finite volume scheme for pricing European options under regime-switching Kou's jump-diffusion model which is governed by a system of partial integro-differential equations (PIDEs). We show that this scheme is consistent, stable and monotone as the mesh sizes in space and time approach zero, hence it ensures the convergence to the solution of continuous problem. Finally, numerical experiments are performed to demonstrate the efficiency, accuracy and robustness of the proposed method.

Xiaoting Gan, Junfeng Yin & Rui Li. (2023). On the Convergence of a Crank-Nicolson Fitted Finite Volume Method for Pricing European Options Under Regime-Switching Kou’s Jump-Diffusion Models. Advances in Applied Mathematics and Mechanics. 15 (5). 1290-1314. doi:10.4208/aamm.OA-2021-0016
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