Modelling of Lévy term structures

Ernst Eberlein

Abstract: Term structure models in the context of credit risk which have been studied in the literature so far are typically models driven by a Brownian motion, or are standard jump diffusions. See Zhou (1997), Schönbucher (1998), or Duffie and Singleton (1999) for examples, and the surveys on credit risk models in Lando (1997), Ammann (1999), and Schönbucher (2000).

A new approach to credit risk based on the term structure methodology of Heath, Jarrow, and Morton (1992) was introduced by Bielecki and Rutkowski (1999, 2000). The Bielecki-Rutkowski model takes the information on rating migration and on credit spreads into account and yields an arbitrage-free model of defaultable bonds. We follow this approach to construct an intensity-based credit risk framework for term structure models driven by Lévy processes.

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