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Finite Difference Method for the Hull–White Partial Differential Equations

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  • Yongwoong Lee

    (Department of International Finance, College of Economics and Business, Hankuk University of Foreign Studies, 81 Oedae-ro, Mohyeon-eup, Cheoin-gu, Yongin-si 17035, Gyeonggi-do, Korea)

  • Kisung Yang

    (School of Finance, College of Business Administration, Soongsil University, 369 Sangdo-ro, Dongjak-gu, Seoul 06978, Korea)

Abstract

This paper reviews the finite difference method (FDM) for pricing interest rate derivatives (IRDs) under the Hull–White Extended Vasicek model (HW model) and provides the MATLAB codes for it. Among the financial derivatives on various underlying assets, IRDs have the largest trading volume and the HW model is widely used for pricing them. We introduce general backgrounds of the HW model, its associated partial differential equations (PDEs), and FDM formulation for one- and two-asset problems. The two-asset problem is solved by the basic operator splitting method. For numerical tests, one- and two-asset bond options are considered. The computational results show close values to analytic solutions. We conclude with a brief comment on the research topics for the PDE approach to IRD pricing.

Suggested Citation

  • Yongwoong Lee & Kisung Yang, 2020. "Finite Difference Method for the Hull–White Partial Differential Equations," Mathematics, MDPI, vol. 8(10), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1719-:d:424436
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    References listed on IDEAS

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    Cited by:

    1. Indu Rani & Chandan Kumar Verma, 2024. "Analyzing Short-Rate Models for Efficient Bond Option Pricing: A Review," SN Operations Research Forum, Springer, vol. 5(3), pages 1-26, September.
    2. Tomohisa Yamakami & Yuki Takeuchi, 2022. "Pricing Bermudan Swaption under Two Factor Hull-White Model with Fast Gauss Transform," Papers 2212.08250, arXiv.org.

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