Lévy copulas: review of recent results

Characterization of dependence of multidimensional Lévy processes using Lévy copulas

This paper suggests to use Lévy copulas 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 kind 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 copu...

Bayesian Estimation of Lévy Copulas for Multivariate Operational Risks

Multivariate Operational Risk: Dependence Modelling with Lévy Copulas

Simultaneous modelling of operational risks occurring in different event type/business line cells poses the challenge for operational risk quantification. Invoking the new concept of Lévy copulas for dependence modelling yields simple approximations of high quality for multivariate operational VAR.

Lévy-copula-driven Financial Processes

Abstract. This paper proposes a general non-Gaussian Ornstein-Uhlenbeck model for a joint financial process based on marginal Lévy measures joined by a Lévy copula. Simulated processes then result from choices of marginal measures and Lévy copulas, with resulting statistics and inferences. Selected for analysis are the 3/2-stable and Gamma marginal Lévy measures, along with Clayton, Gumbel, and...

Lévy copulas: dynamics and transforms of Upsilon-type

Lévy processes and infinitely divisible distributions are increasingly defined in terms of their Lévy measure. In order to describe the dependence structure of a multivariate Lévy measure, Tankov (2003) introduced positive Lévy copulas. Together with the marginal Lévy measures they completely describe multivariate Lévy measures on R+ . In this paper, we show that any such Lévy copula defines it...