Construction and sampling of Archimedean and nested Archimedean Lévy copulas

The class of Archimedean Lévy copulas is considered with focus on the construction and sampling of the corresponding Lévy processes. Furthermore, the class of nested Archimedean Lévy copulas is introduced. This class allows one to model hierarchical dependences between Lévy processes. It also overco...

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Bibliographic Details
Published in:Journal of multivariate analysis 2015-06, Vol.138, p.182-198
Main Authors: Grothe, Oliver, Hofert, Marius
Format: Article
Language:English
Subjects:
(Nested) Archimedean (Lévy) copulas
Algorithms
Lévy copulas
Lévy processes
Mathematical models
Multivariate analysis
Probability distribution
Sampling
Sampling techniques
Studies
Symmetry
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Summary:The class of Archimedean Lévy copulas is considered with focus on the construction and sampling of the corresponding Lévy processes. Furthermore, the class of nested Archimedean Lévy copulas is introduced. This class allows one to model hierarchical dependences between Lévy processes. It also overcomes the symmetry of Archimedean Lévy copulas. Finally, a new sampling algorithm for multivariate Lévy processes with dependence structure specified by either Archimedean or nested Archimedean Lévy copulas is derived from a Marshall–Olkin-type algorithm. In contrast to the widely used conditional sampling method, this algorithm does not require (inverses of) conditional Lévy copulas to be known. It also does not suffer from an asymmetric bias introduced by the conditional sampling method in the Lévy framework.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2014.12.004