On VaR using modified gaussian copula

Abstract

The problem of modeling asset returns is one of the most important issue in finance. People generally use Gaussian processes because of their tractable properties for computation. However, it is well known that asset returns are fat-tailed leading to an underestimation of the risk. One of the most recent proposals is to model the interdependence of asset returns, for example in a portfolio, by means of Copulas and choose marginal distributions with fat tail to fit the single asset returns. The aim of the paper is to show first results concerning the evaluation of Portfolio Value-at-Risk (VaR) using the Gaussian copula, modified by introducing a particular correlation coefficient, and assuming distributions of the Exponential Power Function (E.P.F.) type for the single returns in the portfolio. The new method is a generalization of the RiskMetrics method, which it is close to in the case of Gaussian marginal distributions, while it moves away from it if the return distributions are more fat-tailed. The predictive capacity of the new method is evaluated by means of a backtest on data relating to some financial portfolios and compared with two other methods.