RATING BASED LÉVY LIBOR MODEL. (3rd February 2012)

• Record Type: Journal Article
• Authors: Eberlein, Ernst; Grbac, Zorana
• Is Part Of: Mathematical finance. Volume 23:Number 4(2013:Oct.)
• Page Start: 591
• Page End: 626
• Publication Date: 2012-02-03
• Subjects: credit risk -- ratings -- time‐inhomogeneous Lévy process -- Libor -- conditional Markov chain; Business mathematics -- Periodicals; 332
• DOI: 10.1111/j.1467-9965.2011.00514.x
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract : In this paper, we consider modeling of credit risk within the Libor market models. We extend the classical definition of the default‐free forward Libor rate and develop the rating based Libor market model to cover defaultable bonds with credit ratings. As driving processes for the dynamics of the default‐free and the predefault term structure of Libor rates, time‐inhomogeneous Lévy processes are used. Credit migration is modeled by a conditional Markov chain, whose properties are preserved under different forward Libor measures. Conditions for absence of arbitrage in the model are derived and valuation formulae for some common credit derivatives in this setup are presented.