Tails of correlation mixtures of elliptical copulas

TL;DR

This paper investigates correlation mixtures of elliptical copulas, revealing they exhibit significantly increased tail dependence compared to standard elliptical copulas, impacting risk modeling and estimation.

Contribution

It introduces the concept of correlation mixtures of elliptical copulas, analyzing their tail dependence properties and implications for financial risk modeling.

Findings

Correlation mixtures show larger tail dependence than standard elliptical copulas.

Tail dependence at sub-asymptotic levels exceeds asymptotic limits.

Correlation mixtures of Gaussian copulas are near asymptotic dependent despite asymptotic independence.

Abstract

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.