Swaptions in Libor Market Model with Local Volatility

Wilmott Journal, Vol. 2, No. 3, pp. 135-154, June 2010

Posted: 7 Nov 2010

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: June 1, 2010

Abstract

The Libor Market Model (LMM) describes the evolution of a yield curve through equations for a discrete set of forward rates. In the original version, the rate dynamic was log-normal. The rate dynamic has been extended. The main result presented here is a generic approximation that provides an explicit European swaptions price for local volatilities LMM. The approximation is based on an initial freeze approximation very efficient in the Bond Market Model and an original corrector-type approach. The approximation is strike dependent, allowing a smile calibration. The approximation efficiency is analyzed in details in the displaced diffusion case by comparison to precise Monte Carlo simulations.

Keywords: Explicit Formula, Libor Market Model, Displaced Diffusion, Local Volatility, Smile, Approximation.

JEL Classification: G13, E43, C63

Suggested Citation

Henrard, Marc P. A., Swaptions in Libor Market Model with Local Volatility (June 1, 2010). Wilmott Journal, Vol. 2, No. 3, pp. 135-154, June 2010. Available at SSRN: https://ssrn.com/abstract=1703863

Marc P. A. Henrard (Contact Author)

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