Title
Sampling Nested Archimedean Copulas: with Applications to CDO Pricing,Used
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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 onedimensional function called the generator of the Archimedean copula. In largedimensional 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 largescale simulation studies. Efficiently sampling nested Archimedean copulas requires sampling from certain distributions which are related to the generators of the Archimedean copulas involved via LaplaceStieltjes 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 creditrisky portfolio.
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