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.
General
Imprint: |
Sudwestdeutscher Verlag Fur Hochschulschriften AG
|
Country of origin: |
United States |
Release date: |
June 2010 |
First published: |
June 2010 |
Authors: |
Jan Marius Hofert
|
Dimensions: |
229 x 152 x 12mm (L x W x T) |
Format: |
Paperback - Trade
|
Pages: |
200 |
ISBN-13: |
978-3-8381-1656-3 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Probability & statistics
|
LSN: |
3-8381-1656-9 |
Barcode: |
9783838116563 |
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