Lévy Copulas: Review of recent results

Abstract

We review and extend the now considerable literature on Lévy copulas. First, we focus on Monte Carlo methods and present a new robust algorithm for the simulation of multidimensional Lévy processes with dependence given by a Lévy copula. Next, we review statistical estimation techniques in a parametric and a non-parametric setting. Finally, we discuss the interplay between Lévy copulas and multivariate regular variation and briefly review the applications of Lévy copulas in risk management. In particular, we provide a new easy-to-use sufficient condition for multivariate regular variation of Lévy measures in terms of their Lévy copulas.