The LIBOR Market Model

Abstract

This thesis is devoted to the calibration of the lognormal LIBOR Market Model to caplets and swaptions. Using a Hermite Bessel spline interpolation scheme, calibration of yield curves is performed by fitting to a set of spot rate fixings, forward rate agreements and swaps. Rebonato’s parameterization of instantaneous forward rate volatilities is used to calibrate to caplet volatilities. Instantaneous forward rate correlations are explored by estimating a historical forward rate correlation matrix and by implying them from swaption quotes. We parameterize instantaneous forward rate correlations with Schoenmakers & Coffey’s 3-parameter form and Lutz’ New 5-parameter form and show that the latter outperforms the former. We derive Rebonato’s approximate swaption volatility formula and apply it to a swaption matrix. Caplet volatilities are bootstrapped from flat cap volatilities and a Monte Carlo simulation of the LIBOR Market Model is carried out.