The Lévy Libor model with default risk

Abstract

In this paper we present a model for the dynamic evolution of the term structure of default-free and defaultable interest rates. The model is set in the Libor market model framework but in contrast to the classical diffusion-driven setup, its dynamics are driven by a time-inhomogeneous Levy process which allows us to better capture the real-world dynamics of credit spreads. We present necessary and sufficient conditions for absence of arbitrage in the dynamics of the spreads, and provide pricing formulae for defaultable bonds, credit default swaps and options on credit default swaps in this setup.