TY - JOUR
T1 - High Order Method for Variable Coefficient Integro-Differential Equations and Inequalities Arising in Option Pricing
AU - Sahu , Pradeep Kumar
AU - Patel , Kuldip Singh
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 538
EP - 556
PY - 2023
DA - 2023/05
SN - 20
DO - http://doi.org/10.4208/ijnam2023-1023
UR - https://global-sci.org/intro/article_detail/ijnam/21715.html
KW - Schur polynomials, implicit-explicit schemes, partial integro-differential equations, jump-diffusion models, option pricing.
AB - <p style="text-align: justify;">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.</p>