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Sampling Nested Archimedean Copulas

Name: Sampling Nested Archimedean Copulas
Brand: Sudwestdeutscher Verlag Fur Hochschulschriften AG
SKU: 06961799
Price: 27585 HUF
Availability: InStock
Author: Jan Marius Hofert
ISBN: 9783838116563

with Applications to CDO Pricing

Jan Marius Hofert

Language

English

Book Paperback

Libristo code: 06961799

Publishers Sudwestdeutscher Verlag Fur Hochschulschriften AG, June 2010

Copulas are distribution functions with standard uniform univariate margins. A famous class of copul... Full description

Libristo code: 06961799

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27 585 Ft

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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.