Value at risk forecasts by extreme value models in a conditional duration framework

The analysis of extremes in financial return series is often based on the assumption of independent and identically distributed observations. However, stylized facts such as clustered extremes and serial dependence typically violate the assumption of independence. This has been the main motivation to propose an approach that is able to overcome these difficulties by considering the time between extreme events as a stochastic process. One of the advantages of the method consists in its capability to capture the short-term behavior of extremes without involving an arbitrary stochastic volatility model or a prefiltration of the data, which would certainly affect the estimate. We make use of the proposed model to obtain an improved estimate for the value at risk (VaR). The model is then compared to various competing approaches such as Engle and Marianelli's CAViaR and the GARCH-EVT model. Finally, we present a comparative empirical illustration with transaction data from Bayer AG, a typical blue chip stock from the German stock market index DAX, the DAX index itself and a hypothetical portfolio of international equity indexes already used by other authors.