Estimation of Value at Risk using conditional copula: The choice of copula

This study examines the impact of different types of copula on the performance of weekly VaR estimation for a two-asset portfolio composed of stock indices using a conditional copula methodology. The aim is to find out if the choice of copula is important since Fantazzini (2008) found it not to be. The Gaussian copula, the Student’s t copula and the SJC copula was included in this study based on the recommendations in previous research and their type of tail dependence. In order to investigate the impact of copulas full parametric models were made where the only difference was in the copula used. One-week-ahead out-of-sample VaR forecasts at the 95% and 99% confidence level was estimated for the portfolio by using these models in a moving window technique together with Monte Carlo simulation. The VaR estimation results were similar and suggested that Fantazzini (2008) was correct. However, a study of the tail dependence modelled by the Student’s t copula showed that it was not negligible. Furthermore, a comparison of the tail dependence modelled by the Student’s t copula and the SJC copula indicated that the imposed symmetric tail dependence in the Student’s t copula was not natural. The conclusion is therefore that the choice of copula is important since choosing one of the elliptical copulas would entail an increased model risk and lead to an overall increased risk of error in VaR estimates. (Less)