Swaptions in Libor Market Model with Local Volatility
Marc P. A. Henrard
June 27, 2007
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
Date posted: February 28, 2008 ; Last revised: January 21, 2009
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