An Efficient Localized RBF-FD Method to Simulate the Heston–Hull–White PDE in Finance

Tao Liu, Malik Zaka Ullah, Stanford Shateyi (), Chao Liu and Yanxiong Yang
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Tao Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066000, China
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
Chao Liu: School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066000, China
Yanxiong Yang: Eighth Geological Brigade of Hebei Bureau of Geology and Mineral Resources Exploration, Qinhuangdao 066000, China

Mathematics, 2023, vol. 11, issue 4, 1-15

Abstract: The Heston–Hull–White three-dimensional time-dependent partial differential equation (PDE) is one of the important models in mathematical finance, at which not only the volatility is modeled based on a stochastic process but also the rate of interest is assumed to follow a stochastic dynamic. Hence, an efficient method is derived in this paper based on the methodology of the localized radial basis function generated finite difference (RBF-FD) scheme. The proposed solver uses the RBF-FD approximations on graded meshes along all three spatial variables and a high order time-stepping scheme. Stability is also studied in detail to show under what conditions the proposed method is stable. Computational simulations are given to support the theoretical discussions.

Keywords: graded meshes; stochastic rate of interest; stable; pricing options; Heston–Hull–White PDE (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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