Copula

Quantitative Finance Glossary

A multivariate CDF on [0,1]^d with uniform marginals that joins arbitrary marginals into a joint distribution: by Sklar's theorem F(x_1,ldots,x_d) = C(F_1(x_1),ldots,F_d(x_d)). Decouples marginal modelling from dependence modelling. The Gaussian copula was the workhorse of pre-2008 CDO pricing (Li 2000) and its failure to capture tail dependence — extreme defaults clustering far more than Gaussian implies — was a proximate cause of CDO mispricing in the GFC. Student-t and Clayton/Gumbel Archimedean copulas exhibit non-zero tail dependence.

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