CMS, CMS Spreads and Similar Options in the Multi-Factor HJM Framework

Posted: 7 Dec 2012

See all articles by Pierre Hanton

Pierre Hanton

BNP Paribas Fortis

Marc P. A. Henrard

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

Date Written: November 1, 2012

Abstract

Constant maturity swaps (CMS) and CMS spread options are analyzed in the multi-factor HJM framework. For Gaussian models, which include some Libor Market Models and the G2 model, explicit approximated pricing formulae are provided. Two approximating approaches are proposed: an exact solution to an approximated equation and an approximated solution to the exact equation. The first approach borrows from previous literature on other models; the second approach is new. For this latter, the price approximation errors are smaller than in the previous literature and negligible in practice. These approaches are being used here to price standard CMS and CMS spreads and can be used for some European exotic products.

Keywords: CMS, CMS spread, Heath-Jarrow-Morton, multi-factor model, Gaussian models, G2, Libor Market Model, analytical formula, efficient approximation

Suggested Citation

Hanton, Pierre and Henrard, Marc P. A., CMS, CMS Spreads and Similar Options in the Multi-Factor HJM Framework (November 1, 2012). International Journal of Theoretical and Applied Finance, Vol. 15, No. 7, 2012. Available at SSRN: https://ssrn.com/abstract=2185397

Pierre Hanton

BNP Paribas Fortis ( email )

Brussels
Belgium

Marc P. A. Henrard (Contact Author)

muRisQ Advisory ( email )

Rue du Chemin de fer, 8
Brussels, 1210
Belgium

HOME PAGE: http://murisq.com

OpenGamma ( email )

Albert House
256-260 Old Street
London, EC1V 9DD
United Kingdom

University College London - Department of Mathematics ( email )

Gower Street
London, WC1E 6BT
United Kingdom

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