Bermudan Swaptions in Gaussian HJM One-Factor Model: Analytical and Numerical Approaches

13 Pages Posted: 22 Oct 2008 Last revised: 10 May 2010

See all articles by Marc P. A. Henrard

Marc P. A. Henrard

muRisQ Advisory; OpenGamma; University College London - Department of Mathematics

Date Written: October 20, 2008

Abstract

A popular way to value (Bermudan) swaption in a Hull-White or extended Vasicek model is to use a tree or PDE approach. A more direct approach through iterated numerical integration is developed. 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, the complexity can be reduced to 4pN versus the quadratic complexity (pN)^2 in the tree.

A semi-explicit formula leading to a faster converging implementation is also proposed.

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

JEL Classification: G13, E43

Suggested Citation

Henrard, Marc P. A., Bermudan Swaptions in Gaussian HJM One-Factor Model: Analytical and Numerical Approaches (October 20, 2008). Available at SSRN: https://ssrn.com/abstract=1287982 or http://dx.doi.org/10.2139/ssrn.1287982

Marc P. A. Henrard (Contact Author)

muRisQ Advisory ( email )

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Brussels, 1210
Belgium

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OpenGamma ( email )

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London, EC1V 9DD
United Kingdom

University College London - Department of Mathematics ( email )

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London, WC1E 6BT
United Kingdom

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