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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, EconWPA.
  • 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: http://econwpa.repec.org/eps/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, EconWPA.
    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..
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    Cited by:

    1. 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.

    More about this item

    Keywords

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

    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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