Extremes

, Volume 16, Issue 3, pp 303–324

Jump tail dependence in Lévy copula models

Article

DOI: 10.1007/s10687-012-0162-1

Cite this article as:
Grothe, O. Extremes (2013) 16: 303. doi:10.1007/s10687-012-0162-1
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Abstract

This paper investigates the dependence of extreme jumps in multivariate Lévy 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 Lévy copula alone and that it is independent of marginal Lévy 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.

Keywords

Multivariate Lévy processes Dependence of jumps Nonparametric estimation Strong consistency High frequency financial data Portfolios 

AMS 2000 Subject Classifications

60G51 62G32 91G70 

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Economic and Social StatisticsUniversity of CologneKölnGermany