Über die Vorteilhaftigkeit von Copula-GARCH-Modellen im finanzwirtschaftlichen Risikomanagement

Abstract

This article focuses on two questions: In what circumstances should a Copula- GARCH model be preferred to a correlation-based model? And, where appropriate, what Copula-model parameters should be used? In answer to these two questions, the empirical value at risk and expected shortfall study calculates various forms of investment from a total of 1275 bivariate portfolios composed of the log returns of such forms of investment. The simulations made show that for just one-third of the examined portfolios a Copula-GARCH model could help improve the VaR estimates of the DCC model as a correlation-based benchmark. This proves that this study has not been able to show that Copula models are more advantageous in general over correlation-based ones. At the same time, the empirical Copula-based adjustment test, which has been used in this study, has been weak by comparison as regards its ability to select the optimal model. In almost all cases, the GoF test has produced either an ambivalent or a false recommendation. At the same time, it has been demonstrated that certain descriptive statistics may well be used as decisionmaking aid in favour of a Copula-GARCH model and, respectively, the DCC model. Finally, this study shows that the completely time-dependent mixture of Copulas used in this study for the first time have been of an only low prognosticating quality.