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Error analysis of finite difference scheme for American option pricing under regime-switching with jumps.
- Source :
-
Journal of Computational & Applied Mathematics . Feb2024, Vol. 437, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- This paper mainly focuses on evaluating American options under regime-switching jump-diffusion models (Merton's and Kou's models). An efficient numerical method is designed for the concerned problems. The problem of American option pricing under regime-switching jump-diffusion models can be described as a free-boundary problem or a complementarity problem with integral and differential terms on an unbounded domain. By analyzing the relation of optimal exercise boundaries among several options, we truncate the solving domain of regime-switching jump-diffusion options, and present reasonable boundary conditions. For the integral terms of the truncated model, a composite trapezoidal formula is applied, which guarantees that the integral discretized matrix is a Toeplitz matrix. Meanwhile, a finite difference scheme is proposed for the resulting system, which leads to a linear complementary problem (LCP) with a unique solution. Moreover, we also prove the stability, monotonicity, and consistency of the discretization scheme and estimate the convergence order. In consideration of the characteristics of the discrete matrix, a projection and contraction method is suggested to solve the discretized LCP. Numerical experiments are carried out to verify the efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03770427
- Volume :
- 437
- Database :
- Academic Search Index
- Journal :
- Journal of Computational & Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 172368517
- Full Text :
- https://doi.org/10.1016/j.cam.2023.115484