Rating based Lévy Libor model (Q2851557)

This paper discusses a Lévy Libor model which incorporates credit risk attributed to changes in ratings. It extends a default-free Lévy Libor with a view to modelling defaultable bonds with credit ratings. The migration of credit ratings is modelled by a conditional Markov chain whose states represent different rating classes. The conditional Markov chain under different forward Libor measures is discussed and it is shown that the properties of the conditional Markov chain are preserved under different forward Libor measures. The necessary and sufficient conditions for precluding arbitrage opportunities in the rating-based Lévy Libor model are identified. These condition are presented in Theorem 5.1. Applications of the rating-based Lévy Libor model to value credit derivatives such as defaultable bonds and credit default swaps are discussed. In particular, the valuation results for a defaultable bond and a credit default swap are presented in Proposition 6.1 and Proposition 6.2, respectively.