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Bermudan swaptions in Hull-White one-factor model: analytical and numerical approaches

Author

Listed:
  • Marc Henrard

    (Bank for International Settlements)

Abstract

A popular way to value (Bermudan) swaption in a Hull-White or extended Vasicek model is to use a tree approach. In this note we show that a more direct approach through iterated numerical integration is also possible. A brute force numerical integration would lead to a complexity exponential in the number of exercise dates in the base of the number of points ($p^N$). By carefully choosing the integration points and their order we can reduce it to a complexity $pN^2$ versus a quadratic $(pN)^2$ in the tree. We also provide a semi-explicit formula that leads to a faster converging implementation.

Suggested Citation

  • Marc Henrard, 2005. "Bermudan swaptions in Hull-White one-factor model: analytical and numerical approaches," Finance 0505023, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0505023
    Note: Type of Document - pdf; pages: 9. Draft version, comments welcome. Math Subject Classification MSC2000: 91B28, 91B24, 91B70
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0505/0505023.pdf
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    References listed on IDEAS

    as
    1. Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, University Library of Munich, Germany.
    2. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    3. Marc Henrard, 2003. "Explicit Bond Option Formula In Heath–Jarrow–Morton One Factor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 57-72.
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    Cited by:

    1. Bünyamin Erkan & Jean-Luc Prigent, 2020. "About Long-Term Cross-Currency Bermuda Swaption Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 239-262, June.
    2. Marc Henrard, 2006. "A Semi-Explicit Approach to Canary Swaptions in HJM One-Factor Model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 1-18.

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    More about this item

    Keywords

    Bermudan option; swaption; Hull-White model; one-factor model; numerical integration.;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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