Construction and sampling of Archimedean and nested Archimedean Lévy copulas

Abstract

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.