Sampling Archimedean copulas |
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Authors: | Marius Hofert |
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Affiliation: | Universität Ulm, Institut für Angewandte Analysis, Helmholtzstraße 18, 89069 Ulm, Germany |
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Abstract: | The challenge of efficiently sampling exchangeable and nested Archimedean copulas is addressed. Specific focus is put on large dimensions, where methods involving generator derivatives are not applicable. Additionally, new conditions under which Archimedean copulas can be mixed to construct nested Archimedean copulas are presented. Moreover, for some Archimedean families, direct sampling algorithms are given. For other families, sampling algorithms based on numerical inversion of Laplace transforms are suggested. For this purpose, the Fixed Talbot, Gaver Stehfest, Gaver Wynn rho, and Laguerre series algorithm are compared in terms of precision and runtime. Examples are given, including both exchangeable and nested Archimedean copulas. |
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