Finding an Efficient Computational Solution for the Bates Partial Integro-Differential Equation Utilizing the RBF-FD Scheme

Gholamreza Farahmand, Taher Lotfi (), Malik Zaka Ullah and Stanford Shateyi ()
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Gholamreza Farahmand: Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
Taher Lotfi: Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
Malik Zaka Ullah: Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Stanford Shateyi: Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa

Mathematics, 2023, vol. 11, issue 5, 1-13

Abstract: This paper proposes a computational solver via the localized radial basis function finite difference (RBF-FD) scheme and the use of graded meshes for solving the time-dependent Bates partial integro-differential equation (PIDE) arising in computational finance. In order to avoid facing a large system of discretization systems, we employ graded meshes along both of the spatial variables, which results in constructing a set of ordinary differential equations (ODEs) of lower sizes. Moreover, an explicit time integrator is used because it can bypass the need to solve the large discretized linear systems in each time level. The stability of the numerical method is discussed in detail based on the eigenvalues of the system matrix. Finally, numerical tests revealed the accuracy and reliability of the presented solver.

Keywords: PIDE; stochastic volatility; semi-discretiztion; RBF-FD; Bates model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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