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

Authors


Liang Peng, School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA.
E-mail: peng@math.gatech.edu

Abstract

Abstract.  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.

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