  Correlation mixtures of elliptical copulas arise when the correlation
parameter is driven itself by a latent random process. For such copulas, both
penultimate and asymptotic tail dependence are much larger than for ordinary
elliptical copulas with the same unconditional correlation. Furthermore, for
Gaussian and Student t-copulas, tail dependence at sub-asymptotic levels is
generally larger than in the limit, which can have serious consequences for
estimation and evaluation of extreme risk. Finally, although correlation
mixtures of Gaussian copulas inherit the property of asymptotic independence,
at the same time they fall in the newly defined category of near asymptotic
dependence. The consequences of these findings for modeling are assessed by
means of a simulation study and a case study involving financial time series.
