DEFAULTABLE LÉVY LIBOR RATES AND CREDIT DERIVATIVES

We introduce the intensity-based defaultable Lévy Libor model, which generalizes the default-free Lévy Libor model introduced by Eberlein and Özkan in [The defaultable Lévy term structure: Ratings and restructuring, Mathematical Finance 13(2) (2003) 277–300], and the intensity-based defaultable model presented by Bielecki and Rutkowski in [Credit Risk: Modeling, Valuation and Hedging, Springer Finance (Springer-Verlag, 2002)] by embedding it in the defaultable HJM framework introduced by Eberlein and Özkan in [The defaultable Lévy term structure: Ratings and restructuring, Mathematical Finance 13(2) (2003) 277–300]. We also derive some additional results for defaultable HJM models such as the dynamics of credit spreads. We then go on and model the default-free Libor rates and credit spreads as the primal variable and derive the dynamics of the defaultable Libor rates under the defaultable forward measure. Finally, we derive an explicit formula for options on credit default swaps, using an idea introduced by Raible in [Lévy Processes in finance: Theory, numerics and empirical facts, PhD thesis, University of Freiburg i. Brsg. (2000)].