BFS 2002

Poster Presentation

On the distributional distance between the LIBOR and the swap market models.

Jan Liinev, Damiano Brigo

In this paper we consider the distributional difference between forward swap rates as implied by the lognormal forward-Libor model (LFM) and the lognormal forward-swap model (LSM) respectively. To measure this distributional difference, we resort to a "metric" in the space of distributions, the Kullback-Leibler information (KLI). We explain how the KLI can be used to measure the distance of a given distribution from the lognormal family of densities, and then apply this framework to our models' comparison. The volatility of the projection of the LFM swap-rate distribution onto the lognormal family is compared to a synthetic swap volatility approximation used by the industry. Finally, for some instantaneous covariance parameterizations of the LFM we analyze how the KLI changes according to the parameter values and to the parameterizations themselves, in an attempt to characterize the situations where LFM and LSM are distributionally close, as is often assumed by market practice.