Jump tail dependence in Lévy copula models

This paper investigates the dependence of extreme jumps in multivariate Levy processes. We introduce a measure called jump tail dependence, defined as the probability of observing a large jump in one component of a process given a concurrent large jump in another component. We show that this measure is determined by the Levy copula alone and that it is independent of marginal Levy processes. We derive a consistent nonparametric estimator for jump tail dependence and establish its asymptotic distribution. Regarding the economic relevance of the measure, a simulation study illustrates that jump tail dependence has a substantial impact on financial portfolio distributions and optimal portfolio weights.