Damiano Brigo, Fabio Mercurio, Francesco Rapisarda
In this work we consider different parametric assumptions for the instantaneous covariance structure of the Libor market model. We examine the impact of each parameterization on the evolution of the term structure of volatilities in time, on terminal correlations and on the joint calibration to the caps and swaptions markets.
We present a number of cases of calibration in the Euro market. In particular, we consider calibration to swaptions via a parameterization establishing a controllable one to one correspondence between instantaneous covariance parameters and swaptions volatilities, and assess the possible benefits of smoothing the input swaption matrix before calibrating.
Finally, we hint at the problem of measuring the divergence between the swap rate distribution coming from the Libor model and the exponential family of lognormal densities, this distance being related to the quality of the algebraic approximation replacing Monte Carlo evaluation in the calibration procedure.