Sampling Archimedean copulas

This paper addresses the problem of efficiently sampling exchangeable and nested Archimedean copulas, with specific focus on large dimensions, where methods involving generator derivatives, such as the conditional distribution method, 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.