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Semi-parametric estimation of elliptical distribution in case of high dimensionality

By Irina Pimenova

Abstract

This paper is devoted to the problem of high dimensionality in finance. We consider a joint multivariate density estimator of elliptical distribution which relies on a non-parametric estimation of a generator function. The factor model is employed in order to obtain a consistent covariance matrix estimator. We provide a simulation study that suggests that the considered estimator significantly outperforms the one based on the sample covariance matrix estimator. We also provide an empirical study using an example of a S&P500 portfolio. The returns of the resulted distribution are fat tailed and have a high peak. The comparison with other distributions illustrates the inappropriateness of normal or Student t distribution to fit the financial returns. Calculations of VaR are provided as an example of possible applications

Topics: covariance matrix, high dimensionality, factor models, elliptical distributions, 330 Wirtschaft, ddc:330
Publisher: Humboldt-Universität zu Berlin, Wirtschaftswissenschaftliche Fakultät
Year: 2012
OAI identifier: oai:edoc.hu-berlin.de:18452/14829
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