Characterization of dependence of multidimensional Lévy processes using Lévy copulas

Authors:
Jan Kallsen;Peter Tankov
Affiliations:
HVB-Stiftungsinstitut für Finanzmathematik, Zentrum Mathematik, TU München, Garching bei München, Germany;INRIA Rocquencourt, Le Chesnay Cedex, France and Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VII, Paris Cedex, France
Venue:
Journal of Multivariate Analysis
Year:
2006

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Abstract

This paper suggests Lévy copulas in order to characterize the dependence among components of multidimensional Lévy processes. This concept parallels the notion of a copula on the level of Lévy measures. As for random vectors, a version of Sklar's theorem states that the law of a general multivariate Lévy process is obtained by combining arbitrary univariate Lévy processes with an arbitrary Lévy copula. We construct parametric families of Lévy copulas and prove a limit theorem, which indicates how to obtain the Lévy copula of a multivariate Lévy process X from the ordinary copula of the random vector Xt for small t.