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

Author

Listed:
  • 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)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2234-:d:1437367
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    References listed on IDEAS

    as
    1. John Hull & Alan White, 2001. "The General Hull–White Model and Supercalibration," Financial Analysts Journal, Taylor & Francis Journals, vol. 57(6), pages 34-43, November.
    2. 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.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    5. Cao, Jiling & Lian, Guanghua & Roslan, Teh Raihana Nazirah, 2016. "Pricing variance swaps under stochastic volatility and stochastic interest rate," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 72-81.
    6. 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.
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