Characterization of dependence of multidimensional Lévy processes using Lévy copulas
نویسندگان
چکیده
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 copula. We construct parametric families of Lévy copulas and prove a limit theorem, which indicates how to obtain the Lévy copula of a multidimensional Lévy process X from the ordinary copulas of the random vectors Xt for fixed t.
منابع مشابه
Lévy copulas: review of recent results
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 mult...
متن کاملMultivariate 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.
متن کاملLévy-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...
متن کاملLévy 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...
متن کامل