Efficient Scheme for the Economic Heston–Hull–White Problem Using Novel RBF-FD Coefficients Derived from Multiquadric Function Integrals

Tao Liu, Zixiao Zhao, Shiyi Ling, Heyang Chao, Hasan Fattahi Nafchi and Stanford Shateyi ()
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Tao Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Zixiao Zhao: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Shiyi Ling: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Heyang Chao: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
Hasan Fattahi Nafchi: Department of Accounting, Faculty of Administrative Sciences and Economics, University of Isfahan, Isfahan 81746-73441, Iran
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, 2024, vol. 12, issue 14, 1-15

Abstract: This study presents an efficient method using the local radial basis function finite difference scheme (RBF-FD). The innovative coefficients are derived from the integrals of the multiquadric (MQ) function. Theoretical convergence rates for the coefficients used in function derivative approximation are provided. The proposed scheme utilizes RBF-FD estimations on three-point non-uniform stencils to construct the final approximation on a tensor grid for the 3D Heston–Hull–White (HHW) PDE, which is relevant in economics and mathematical finance. Numerical evidence and comparative analyses validate the results and the proposed scheme.

Keywords: three-point stencil; HHW PDE; interest rate; financial option pricing; RBF-FD; integral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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