Comparison of Selected Value-at-Risk Models

In this diploma thesis we compare the most prominent nonparametric, parametric and semi-parametric Value-at-Risk (VaR) models for two portfolios - one long and the other short in the PX index. In the nonparametric class we investigate the historical simulation and the weighted historical simulation methods. Out of the various parametric approaches that have been proposed in the literature, we examine the GARCH-type models. In the semi-parametric category we focus on the filtered historical simulation method and models based on the extreme value theory. Results of our empirical analysis have four implications. First, the models based on the historical simulation and the weighted historical simulation methods are inadequate because they lack a proper specification of volatility dynamics. Second, the assumption of the normal conditional distribution in the parametric approach is implausible. Third, the parametric models with the fat-tailed skewed Student distribution and the semi-parametric models can be regarded as adequate. Finally, the regulatory back-testing procedure could be flawed since it tests only for correct unconditional coverage and just assumes that VaR violations are independent. However, we argue that the independence should be tested as well