Extreme Value Copulas and Tail Dependence

The copula function is a multivariate distribution for which the marginal distribution of each variable is uniform. Copulas are used to specify dependence between two or more random variables. The main appeal of copulas is that by using them you can model the correlation structure and the marginals (i.e. the distribution of each of your random variables) separately. Being the limits of copulas of component wise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise naturally in the domain of extreme-value theory, they can also be a convenient choice to model general positive dependence structures. In this paper, we consider extreme value copulas and examine tail dependence coefficient (TDC) of them. Also, by using the copula modeling, we estimate the TDC through the analysis of real insurance dataset