Calibration of the LIBOR Market Model: Three Prescriptions

Abstract

Pricing of European or even exotic (but without early exercise feature) interest rate and swap options in LIBOR market model can be easily performed in so called Monsieur Jourdain approach. The general concept of Monsieur Jourdain approach is such, that all interest rate options without early exercise feature follow the Black-Merton-Scholes model. To this end we construct a set of building blocks consisting of volatilities of forward Libor rates and correlation parameters. A prescription for how to price a large class of instruments using forward Libor volatilities and the yield curve will be presented. Instantaneous volatilities are not used for model calibration and so the procedure is quite straightforward. In the paper we present three simple calibrations of the LIBOR market model useful in pricing.