Abstract

http://ssrn.com/abstract=1098420
 
 

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Swaptions in Libor Market Model with Local Volatility


Marc P. A. Henrard


OpenGamma

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.

Number of Pages in PDF File: 16

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

JEL Classification: G13, E43, C63

working papers series


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Date posted: February 28, 2008 ; Last revised: January 21, 2009

Suggested Citation

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

Contact Information

Marc P. A. Henrard (Contact Author)
OpenGamma ( email )
185 Park Street
London, SE1 9BL
United Kingdom
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