Modelling Asymmetric Dependence Using Copula Functions: An Application to Value-at-Risk in the Energy Sector
46 Pages Posted: 29 Jun 2009
Date Written: June 25, 2009
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.
Keywords: copula functions, forecasting, value-at-risk
JEL Classification: C32, C52, C53, G17, Q43
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