Sampling Nested Archimedean Copulas : with Applications to CDO Pricing

Hofert, Jan Marius

ISBN 10: 3838116569 / ISBN 13: 9783838116563

Published by Südwestdeutscher Verlag für Hochschulschriften, 2010

About this Item

Zustand: Sehr gut | Sprache: Englisch | Produktart: Bücher | 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.

Seller Inventory # 7558108/2

Bibliographic Details

• Title: Sampling Nested Archimedean Copulas : with Applications to CDO Pricing
• Publisher: Südwestdeutscher Verlag für Hochschulschriften
• Publication Date: 2010
• Language: English
• ISBN 10: 3838116569
• ISBN 13: 9783838116563
• Binding: Soft cover
• Condition: Sehr gut
• Seller catalogs:
  • Bücher

About this title

Synopsis

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.

About the Author

Jan Marius Hofert was born in Friedrichshafen, Germany, on Mai 2, 1980. He completed a Master of Science in Mathematics from Syracuse University and a Diploma in Economathematics, as well as a Doctor of Philosophy in Mathematics, from Ulm University. He is currently a postdoc in the Department of Mathematics at ETH Zurich.