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.