The Lévy LIBOR model

Models driven by Lévy processes are attractive because of their greater flexibility compared to classical diffusion models. First we derive the dynamics of the LIBOR rate process in a semimartingale as well as a Lévy Heath-Jarrow-Morton setting. Then we introduce a Lévy LIBOR market model. In order to guarantee positive rates, the LIBOR rate process is constructed as an ordinary exponential. Via backward induction we get that the rates are martingales under the corresponding forward measures. An explicit formula to price caps and floors which uses bilateral Laplace transforms is derived.

Authors and Affiliations

1. Department of Mathematical Stochastics, University of Freiburg, Eckerstraße 1, 79104, Freiburg, Germany

   Ernst Eberlein

2. Freiburg Center for Data Analysis and Modeling, University of Freiburg, Eckerstraße 1, 79104, Freiburg, Germany

   Fehmi Özkan

Corresponding author

Correspondence to Ernst Eberlein.

JEL Classification:

E43, G13

Mathematics Subject Classification (2000):

60H30, 91B28, 60G51

This research has been supported by a grant from the Deutsche Forschungsgemeinschaft (Eb 66/7-2 and 7-3). Our special thanks go to Wolfgang Schmidt for discussions on the use of LIBOR models in practice and for providing some data. We also thank Wolfgang Kluge as well as an anonymous referee for critical remarks which helped to improve the paper considerably.

Manuscript received: December 2002; final version received: June 2004

Reprints and permissions