Construction and sampling of Archimedean and nested Archimedean Levy copulas

The class of Archimedean Levy copulas is considered with focus on the construction and sampling of the corresponding Levy processes. Furthermore, the class of nested Archimedean Levy copulas is introduced. This class allows one to model hierarchical dependences between Levy processes. It also overcomes the symmetry of Archimedean Levy copulas. Finally, a new sampling algorithm for multivariate Levy processes with dependence structure specified by either Archimedean or nested Archimedean Levy 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 Levy copulas to be known. It also does not suffer from an asymmetric bias introduced by the conditional sampling method in the Levy framework. (C) 2014 Elsevier Inc. All rights reserved.