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Volume 20, Issue 4
High Order Method for Variable Coefficient Integro-Differential Equations and Inequalities Arising in Option Pricing

Pradeep Kumar Sahu & Kuldip Singh Patel

DOI: 10.4208/ijnam2023-1023

Int. J. Numer. Anal. Mod., 20 (2023), pp. 538-556.

Published online: 2023-05

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  • 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.

  • Keywords

Schur polynomials, implicit-explicit schemes, partial integro-differential equations, jump-diffusion models, option pricing.

  • AMS Subject Headings

65M06, 65M12, 91G20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-20-538, author = {Sahu , Pradeep Kumar and Patel , Kuldip Singh}, title = {High Order Method for Variable Coefficient Integro-Differential Equations and Inequalities Arising in Option Pricing}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2023}, volume = {20}, number = {4}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2023-1023}, url = {http://global-sci.org/intro/article_detail/ijnam/21715.html} }
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 -

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.

Sahu , Pradeep Kumar and Patel , Kuldip Singh. (2023). High Order Method for Variable Coefficient Integro-Differential Equations and Inequalities Arising in Option Pricing. International Journal of Numerical Analysis and Modeling. 20 (4). 538-556. doi:10.4208/ijnam2023-1023
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