Multivariate tail copula: modeling and estimation

In general, risk of an extreme outcome in financial markets can be expressed as a function of the tail copula of a high-dimensional vector after standardizing marginals. Hence it is of importance to model and estimate tail copulas. Even for moderate dimension, nonparametrically estimating a tail copula is very inefficient and fitting a parametric model to tail copulas is not robust. In this paper we propose a semi-parametric model for tail copulas via an elliptical copula. Based on this model assumption, we propose a novel estimator for the tail copula, which proves favourable compared to the empirical tail copula, both theoretically and empirically