Constructing hierarchical Archimedean copulas with Lévy subordinators

Authors:
Christian Hering;Marius Hofert;Jan-Frederik Mai;Matthias Scherer
Affiliations:
Ulm University, Institute of Number Theory and Probability Theory, Helmholtzstraíe 18, 89081 Ulm, Germany;Ulm University, Institute of Number Theory and Probability Theory, Helmholtzstraíe 18, 89081 Ulm, Germany;Technische Universität München, HVB Stiftungsinstitut für Finanzmathematik, Boltzmannstraíe 3, 85748 Garching, Germany;Technische Universität München, HVB Stiftungsinstitut für Finanzmathematik, Boltzmannstraíe 3, 85748 Garching, Germany
Venue:
Journal of Multivariate Analysis
Year:
2010

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Abstract

A probabilistic interpretation for hierarchical Archimedean copulas based on Levy subordinators is given. Independent exponential random variables are divided by group-specific Levy subordinators which are evaluated at a common random time. The resulting random vector has a hierarchical Archimedean survival copula. This approach suggests an efficient sampling algorithm and allows one to easily construct several new parametric families of hierarchical Archimedean copulas.