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

Fitted Finite Volume Method for Pricing American Options under Regime-Switching Jump-Diffusion Models Based on Penalty Method
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Year:    2020

Author:    Xiaoting Gan, Jun-Feng Yin, Rui Li

Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2019-0017

Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 3 : pp. 748–773

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

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

Author Details

Xiaoting Gan

Jun-Feng Yin

Rui Li

  1. Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization

    Gan, Xiaoting | Chen, Xiaolin | Xu, Dengguo

    Taiwanese Journal of Mathematics, Vol. 26 (2022), Iss. 1

    https://doi.org/10.11650/tjm/210803 [Citations: 1]

  2. Penalty method for indifference pricing of American option in a liquidity switching market

    Gyulov, Tihomir B. | Koleva, Miglena N.

    Applied Numerical Mathematics, Vol. 172 (2022), Iss. P.525

    https://doi.org/10.1016/j.apnum.2021.11.002 [Citations: 9]