CMS Swaps and Caps in One-Factor Gaussian Models

9 Pages Posted: 14 May 2007 Last revised: 12 Feb 2008

See all articles by Marc P. A. Henrard

Marc P. A. Henrard

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

Date Written: 1 February 2008

Abstract

An approximation approach to Constant Maturity Swaps (CMS) pricing in the separable one-factor Gaussian LMM and HJM models is presented. The approximation used is a Taylor expansion on the swap rate as a function of a random variable which is intuitively similar to a (short) rate. This approach is different from the standard approach in CMS where the discounting is written as a function of the swap rate. The approximation is very efficient. A similar approach can be used to price CMS caps and floors.

Keywords: CMS, CMS caps, Libor Market Model, Bond Market Model, one factor, separability, approximation

JEL Classification: G13, E43, C63

Suggested Citation

Henrard, Marc P. A., CMS Swaps and Caps in One-Factor Gaussian Models (1 February 2008). Available at SSRN: https://ssrn.com/abstract=985551 or http://dx.doi.org/10.2139/ssrn.985551

Marc P. A. Henrard (Contact Author)

muRisQ Advisory ( email )

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OpenGamma ( email )

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University College London - Department of Mathematics ( email )

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