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

by Krassimir Kostadinov of the Munich University of Technology

April 10, 2005

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 coefficients using the whole sample of observations and the non-linear (tail) dependence coefficients using only the extreme observations. We provide theoretical as well as numerical support for our method.

JEL Classification: G11, G21.

AMS Classification: 62G32, 62H12, 62H20, 91B28.

Keywords: elliptical copula estimation, heavy-tailed risk factors, portfolio credit risk, tail dependence.

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