CMS swaps in separable one-factor Gaussian LLM and HJM model

Henrard, Marc (2007): CMS swaps in separable one-factor Gaussian LLM and HJM model. Unpublished.

Abstract

An approximation approach to Constant Maturity Swaps (CMS) pricing in the separable one-factor Gaussian LLM 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.

• Item Type: MPRA Paper
• Institution: Bank for International Settlements
• Language: English
• Keywords: CMS swap; LLM model; HJM model; one factor; approximation
• Subjects: G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods and Programming > C63 - Computational Techniques; Simulation Modeling ; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E43 - Determination of Interest Rates; Term Structure of Interest Rates

References

Brody, D.~C. and Hughston, L.~P. (2004). Chaos and coherence: a new framework for interest-rate modelling. Proc. R. Soc. Lond. A., 460:85--110.

Hagan, P.~S. (2003). Convexity conundrums: Pricing cms swaps, caps, and floors. Wilmott Magazine, pages 38--44.

Heath, D., Jarrow, R., and Morton, A. (1992). Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation. Econometrica, 60(1):77--105.

Henrard, M. (2003). Explicit bond option and swaption formula in Heath-Jarrow-Morton one-factor model. International Journal of Theoretical and Applied Finance, 6(1):57--72.

Henrard, M. (2005). Swaptions: 1 price, 10 deltas, and ... 6 1/2 gammas. Wilmott Magazine, pages 48--57.

Henrard, M. (2006). A semi-explicit approach to {C}anary swaptions in {HJM} one-factor model. Applied Mathematical Finance, 13(1):1--18.

Henrard, M. (2007). Skewed Libor Market Model and Gaussian HJM explicit approaches to rolled deposit options. The Journal of Risk}, 9(4), to appear. Preprint available at SSRN: http://ssrn.com/abstract=956849.

Hull, J.~C. (2006). Options, futures, and other derivatives. Prentice Hall, sixth edition.

Hunt, P.~J. and Kennedy, J.~E. (2004). Financial Derivatives in Theory and Practice. Wiley series in probability and statistics. Wiley, second edition.

Pelsser, A., Pietersz, R., and van Regenmortel, M. (2004). Fast drift-approximated pricing in bgm model. Journal of Computational Finance, 8(1):93--124.