Sampling Nested Archimedean Copulas

with Applications to CDO Pricing

von Jan Marius Hofert

200 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

Copulas are distribution functions with standard uniform univariate margins. A famous class of copulas consists of Archimedean copulas, which are constructed by a one-dimensional function called the generator of the Archimedean copula. In large-dimensional applications the symmetry of Archimedean copulas is often considered to be a drawback. By nesting Archimedean copulas at different levels, one obtains the more general and flexible class of nested Archimedean copulas. The present work explores these copulas. In particular, efficient sampling algorithms, especially suited for large dimensions, are presented. From the practitioner's point of view, fast sampling algorithms are required for large-scale simulation studies. Efficiently sampling nested Archimedean copulas requires sampling from certain distributions which are related to the generators of the Archimedean copulas involved via Laplace-Stieltjes transforms. The work at hand presents efficient strategies for sampling these distributions. As an application, a pricing model for collateralized debt obligations is developed which precisely captures the given hierarchical structure of such a credit-risky portfolio.

• Themen: Mathematik und Naturwissenschaften Mathematik Wahrscheinlichkeitsrechnung und Statistik
• ISBN: 9783838116563
• Sprache: Englisch
• Erscheinungsdatum: 20.04.2010
• Größe: 220 x 150 mm
• Verlag: Südwestdeutscher Verlag für Hochschulschriften