Swaptions in Libor Market Model with Local Volatility

16 Pages Posted: 28 Feb 2008 Last revised: 21 Jan 2009

Marc P. A. Henrard

OpenGamma; University College London - Department of Mathematics

Multiple version iconThere are 2 versions of this paper

Date Written: June 27, 2007

Abstract

The original Libor Market Model (LMM) has been extended to several dynamics (or local volatilities) for the underlying Libor rates. The main result presented here is a generic approximation that provides an explicit swaptions price for local volatilities LMM. The approximation is base on an initial freeze approximation very efficient in the Bond Market Model and a corrector or Runge-Kutta approach. The approximation is not done at the path level but at the global level for a given strike allowing a smile calibration. The approximation efficiency is analyzed in details in the displaced diffusion case; it is analyzed by comparison to precise Monte Carlo simulations.

Keywords: Explicit formula, Libor Market Model, displaced diffusion, local volatility, smile, approximation, calibration

JEL Classification: G13, E43, C63

Suggested Citation

Henrard, Marc P. A., Swaptions in Libor Market Model with Local Volatility (June 27, 2007). Available at SSRN: https://ssrn.com/abstract=1098420 or http://dx.doi.org/10.2139/ssrn.1098420

Marc P. A. Henrard (Contact Author)

OpenGamma ( email )

107 Leadenhall Street - 5th floor
London, EC3A 4AF
United Kingdom

University College London - Department of Mathematics ( email )

Gower Street
London, WC1E 6BT
United Kingdom

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