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

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Author Info

  • 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.

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File URL: http://128.118.178.162/eps/fin/papers/0505/0505023.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0505023.

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Length: 9 pages
Date of creation: 30 May 2005
Date of revision:
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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Web page: http://128.118.178.162

Related research

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

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References

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  1. Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, EconWPA.
  2. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
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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.

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