When it comes to modeling multivariate risks, approaches based on special multivariate parametric distributions such as the multivariate normal distribution are not fully satisfying since only a limited amount of distributional shapes can be represented. This thesis studies a more flexible approach utilizing copulas, in particular the extendible Archimedean copulas and their properties. Due to their probabilistic notion, sampling of extendible Archimedean copulas is possible. Both the probabilistic interpretation and the sampling algorithm are presented. These results enable the application of extendible Archimedean copulas as models for a credit portfolio. The derivation of the portfolio loss distribution is demonstrated in detail. Furthermore, a(n infinitely) large credit portfolio approximation is established, resulting in a more convenient loss distribution.     «

When it comes to modeling multivariate risks, approaches based on special multivariate parametric distributions such as the multivariate normal distribution are not fully satisfying since only a limited amount of distributional shapes can be represented. This thesis studies a more flexible approach utilizing copulas, in particular the extendible Archimedean copulas and their properties. Due to their probabilistic notion, sampling of extendible Archimedean copulas is possible. Both the probabilis...     »