Swaptions in Libor Market Model with Local Volatility
16 Pages Posted: 28 Feb 2008 Last revised: 21 Jan 2009
Date Written: 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.
Keywords: Explicit formula, Libor Market Model, displaced diffusion, local volatility, smile, approximation, calibration
JEL Classification: G13, E43, C63
Suggested Citation: Suggested Citation