Modelling Asymmetric Dependence Using Copula Functions: An application to Value-at-Risk in the Energy Sector
In this paper I have used copula functions to forecast the Value-at-Risk (VaR) of an equally weighted portfolio comprising a small cap stock index and a large cap stock index for the oil and gas industry. The following empirical questions have been analyzed: (i) are there nonnormalities in the marginals? (ii) are there nonnormalities in the dependence structure? (iii) is it worth modelling these nonnormalities in risk- management applications? (iv) do complicated models perform better than simple models? As for questions (i) and (ii) I have shown that the data do deviate from the null of normality at the univariate, as well as at the multivariate level. When considering the dependence structure of the data I have found that asymmetries show up in their unconditional distribution, as well as in their unconditional copula. The VaR forecasting exercise has shown that models based on Normal marginals and/or with symmetric dependence structure fail to deliver accurate VaR forecasts. These findings confirm the importance of nonnormalities and asymmetries both in-sample and out-of-sample.