CMS Spread Options and Similar Options in Multi-Factor HJM Framework

16 Pages Posted: 14 May 2010

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: May 10, 2010

Abstract

Constant maturity swaps (CMS), CMS spreads and similar products are analyzed in multi-factor HJM models. For Gaussian models, which include some Libor Market Models and the G2 model, explicit approximated formula are provided. The approximations are done through two different approaches: an exact solution to an approximated equation and an approximated solution to the exact equation. The first approach has been used previously in the literature for other models, the second is new. The approximations provide prices with error less than 0.02 basis point for the best approach; this is better than the previous literature and negligible in practice. The approach can be used to price standard CMS and CMS spreads and also for similar exotic products.

Keywords: Constant Maturity Swap, CMS spread, multi-factor, HJM

JEL Classification: G13, E43, C63

Suggested Citation

Hanton, Pierre and Henrard, Marc P. A., CMS Spread Options and Similar Options in Multi-Factor HJM Framework (May 10, 2010). Available at SSRN: https://ssrn.com/abstract=1604389 or http://dx.doi.org/10.2139/ssrn.1604389

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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