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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Tao Liu & Malik Zaka Ullah & Stanford Shateyi & Chao Liu & Yanxiong Yang, 2023. "An Efficient Localized RBF-FD Method to Simulate the Heston–Hull–White PDE in Finance," Mathematics, MDPI, vol. 11(4), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:833-:d:1059906
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    References listed on IDEAS

    as
    1. Malik Zaka Ullah, 2019. "Numerical Solution of Heston-Hull-White Three-Dimensional PDE with a High Order FD Scheme," Mathematics, MDPI, vol. 7(8), pages 1-13, August.
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    7. Asghar Rahimi & C.A.Elyas Shivanian & Saeid Abbasbandy & Mubashir Qayyum, 2022. "Analysis of New RBF-FD Weights, Calculated Based on Inverse Quadratic Functions," Journal of Mathematics, Hindawi, vol. 2022, pages 1-7, April.
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    Cited by:

    1. Malik Zaka Ullah & Abdullah Khamis Alzahrani & Hashim Mohammed Alshehri & Stanford Shateyi, 2023. "Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in Finance," Mathematics, MDPI, vol. 11(12), pages 1-12, June.
    2. Tao Liu & Zixiao Zhao & Shiyi Ling & Heyang Chao & Hasan Fattahi Nafchi & Stanford Shateyi, 2024. "Efficient Scheme for the Economic Heston–Hull–White Problem Using Novel RBF-FD Coefficients Derived from Multiquadric Function Integrals," Mathematics, MDPI, vol. 12(14), pages 1-15, July.

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