A Semi-Explicit Approach to Canary Swaptions in HJM One-Factor Model

Economics Working Paper Archive No. 0310008

14 Pages Posted: 31 Dec 2004

See all articles by Marc P. A. Henrard

Marc P. A. Henrard

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

Multiple version iconThere are 2 versions of this paper

Date Written: December 25, 2004

Abstract

Leveraging the explicit formula for European swaptions and coupon-bond options in HJM one-factor model, we develop a semi-explicit formula for 2-Bermudan options (also called Canary options). We first extend the European swaption formula to future times. So equipped, we are able to reduce the valuation of a 2-Bermudan swaption to a single numerical integration at the first expiry date. In that integration the most complex part of the embedded European swaptions valuation has been simplified to perform it only once and not for every point. In a special but very common in practice case, we also provide a semi-explicit formula. Those results lead to a significantly more precise implementation of swaption valuation. The improvements extend even more favorable to sensitivity calculations.

Keywords: Bermudan option, swaption, bond option, HJM model, Hull-White model, one-factor model, explicit formula, numerical integration

JEL Classification: G13, E43

Suggested Citation

Henrard, Marc P. A., A Semi-Explicit Approach to Canary Swaptions in HJM One-Factor Model (December 25, 2004). Economics Working Paper Archive No. 0310008. Available at SSRN: https://ssrn.com/abstract=641941 or http://dx.doi.org/10.2139/ssrn.641941

Marc P. A. Henrard (Contact Author)

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OpenGamma ( email )

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University College London - Department of Mathematics ( email )

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