Pricing American Options under Regime-Switching Model with a Crank-Nicolson Fitted Finite Volume Method
Year: 2020
Author: Xiaoting Gan, Junfeng Yin
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 3 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.170919.221219
East Asian Journal on Applied Mathematics, Vol. 10 (2020), Iss. 3 : pp. 499–519
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: American option pricing regime switching fitted finite volume method Crank-Nicolson scheme.
Author Details
-
Primal‐dual active set algorithm for valuating American options under regime switching
Song, Haiming | Xu, Jingbo | Yang, Jinda | Li, YutianNumerical Methods for Partial Differential Equations, Vol. 40 (2024), Iss. 5
https://doi.org/10.1002/num.23104 [Citations: 0] -
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, DengguoTaiwanese Journal of Mathematics, Vol. 26 (2022), Iss. 1
https://doi.org/10.11650/tjm/210803 [Citations: 1] -
A second-order ADI method for pricing options under fractional regime-switching models
Wang, Ming-Kai | Wang, Cheng | Yin, Jun-FengNetworks and Heterogeneous Media, Vol. 18 (2023), Iss. 2 P.647
https://doi.org/10.3934/nhm.2023028 [Citations: 1] -
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] -
A Preconditioned Iterative Method for a Multi-State Time-Fractional Linear Complementary Problem in Option Pricing
Chen, Xu | Gong, Xinxin | Lei, Siu-Long | Sun, YoufaFractal and Fractional, Vol. 7 (2023), Iss. 4 P.334
https://doi.org/10.3390/fractalfract7040334 [Citations: 2]