Semi-Parametric Models for the Multivariate Tail Dependence Function - the Asymptotically Dependent Case

In general, the risk of joint extreme outcomes in financial markets can be expressed as a function of the tail dependence function of a high-dimensional vector after standardizing marginals. Hence, it is of importance to model and estimate tail dependence functions. Even for moderate dimension, non-parametrically estimating a tail dependence function is very inefficient and fitting a parametric model to tail dependence functions is not robust. In this paper, we propose a semi-parametric model for (asymptotically dependent) tail dependence functions via an elliptical copula. Under this model assumption, we propose a novel estimator for the tail dependence function, which proves favourable compared to the empirical tail dependence function estimator, both theoretically and empirically. Copyright (c) Board of the Foundation of the Scandinavian Journal of Statistics 2008.