Non-parametric Estimation of Elliptical Copulae with Application to Credit Risk

Abstract

This paper develops a method for statistical estimation of the dependence structure of financial assets. As we are interested mainly in applications to credit risk, our approach focuses directly on the copula function of a random vector and works independently of any marginal assumptions. We use the class of elliptical copulas, which provide a natural extension to the standard for the practice Gaussian copula and a flexible model for joint extreme events. We calibrate the linear correlation coe#cients using the whole sample of observations and the non-linear (tail) dependence coe#cients using only the extreme observations. We provide theoretical as well as numerical support for our method