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

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

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Marc Henrard (Bank for International Settlements)

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Marc Henrard

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

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Length: 9 pages
Date of creation: 30 May 2005
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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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Find related papers by JEL classification:
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates

This paper has been announced in the following NEP Reports:

NEP-ALL-2005-06-05 (All new papers)
NEP-CMP-2005-06-05 (Computational Economics)
NEP-FIN-2005-06-05 (Finance)
NEP-MAC-2005-06-05 (Macroeconomics)

References listed on IDEAS
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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. [Downloadable!] (restricted)
Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, EconWPA. [Downloadable!]

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Marc Henrard, 2006. "A Semi-Explicit Approach to Canary Swaptions in HJM One-Factor Model," Applied Mathematical Finance, Taylor and Francis Journals, vol. 13(1), pages 1-18, March. [Downloadable!] (restricted)

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