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Jump tail dependence in Lévy copula models

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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.

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Authors and Affiliations

  1. Department of Economic and Social Statistics, University of Cologne, Albertus-Magnus-Platz, 50923, Köln, Germany

    Oliver Grothe

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  1. Oliver Grothe
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Correspondence to Oliver Grothe.

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Grothe, O. Jump tail dependence in Lévy copula models. Extremes 16, 303–324 (2013). https://doi.org/10.1007/s10687-012-0162-1

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  • DOI: https://doi.org/10.1007/s10687-012-0162-1

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