Copulae in Mathematical and Quantitative Finance by Piotr Jaworski Fabrizio Durante & Wolfgang Karl Härdle

Author:Piotr Jaworski, Fabrizio Durante & Wolfgang Karl Härdle
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

For n = 2 formula (7.7) was widely used to construct copulas with given 2-margins (see, for example, [12, 13, 53]). Furthermore, if copulas C 0, C 1 and C 2 are absolutely continuous, then D is a vine 3-copula (compare [5]). For n > 2 we have the following link with vine copulas:

Proposition 7.7.

If C 0 is an n-variate vine copula and are absolutely continuous bivariate copulas, then the copula D given by (7.7) is a vine copula. Moreover D is represented by a sequence of n trees with T 1 having the first node of degree n and n nodes of degree 1 and the other T i ’s being the same as in the representation of C 0 .

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