High Order Method for Variable Coefficient Integro-Differential Equations and Inequalities Arising in Option Pricing
Year: 2023
Author: Pradeep Kumar Sahu, Kuldip Singh Patel
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 4 : pp. 538–556
Abstract
In this article, the implicit-explicit (IMEX) compact schemes are proposed to solve the partial integro-differential equations (PIDEs), and the linear complementarity problems (LCPs) arising in option pricing. A diagonally dominant tri-diagonal system of linear equations is achieved for a fully discrete problem by eliminating the second derivative approximation using the variable itself and its first derivative approximation. The stability of the fully discrete problem is proved using Schur polynomial approach. Moreover, the problem’s initial condition is smoothed to ensure the fourth-order convergence of the proposed IMEX compact schemes. Numerical illustrations for solving the PIDEs and the LCPs with constant and variable coefficients are presented. For each case, obtained results are compared with the IMEX finite difference scheme, and it is observed that proposed approach significantly outperforms the finite difference scheme.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1023
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 4 : pp. 538–556
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Schur polynomials implicit-explicit schemes partial integro-differential equations jump-diffusion models option pricing.