Prediction of Volatility and Value at Risk with Copulas for Portfolios of Commodities

Abstract: Value at Risk (VaR) is a popular measurement for valuing the risk exposure. Correct estimates of VaR are essential in order to properly be able to monitor the risk. This thesis examines a copula approach for estimating VaR for portfolios of commodities. The predictions are made from a semi- parametric model with Monte Carlo methods. The underlying model is constructed by choosing the best fit from different (E)GARCH- models for margins and some of the most common Archimedean and Elliptical copulas for the dependence. None of the copulas in the scope gave a good fit to the data for the dependence. However, the copula with the best fit was the t-copula, which later was compared with the normal copula, the variance-covariance method and the method with historical observations. The compari- son was done with Kupiec’s test for correct number of VaR breaks and Christoffersen’s test for independent breaks. The results showed that none of the models in scope performed well, although the copula approach followed the data better. Backtest- ing suggested that the copula models overestimated the risk, resulting in too few VaR-breaks that also were clustered. The conclusion was that other copulas would be needed to appro- priately model the dependence, or that more sophisticated modeling methods in general should be used.