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

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