Über die bedingte/gefilterte historische Simulation und nicht-Gauß'schen Modelle im quantitativen Risikomanagement

Abstract

In recent years value-at-risk evolved to a widely spread concept for measuring risks. One possibility to calculate the value-at-risk is the usage of a GARCH- or EWMA-process in combination with a historical simulation and adjustment of historical data to reflect the difference between the historical volatility of the market variable and its current volatility. Another way to specify this measure is to apply the RiskMetrics variance model to the historical simulation, so that declining weigths are applied to past returns. One can also assess the value-at-risk by choosing any probability distribution for the data and using a transformation to obtain a multivariate normal distribution. The necessary parameters are hereby provided by a updating scheme such as GARCH time series. Finally, by circumventing the assumption of normally distributed data and modeling the volatility of the exchange rates by a GARCH-process, the two most frequent points of criticism when calculating the value-at-risk are countered in advance. This diploma thesis illustrates these approaches with the help of daily exchange rates of twelve different currencies and a comparison is carried out.