Value at Risk estimation : A comparison between different models

Abstract: In this thesis the performance of the quantile based CAV iaR models is evaluated and compared with GARCH models for predicting the Value at Risk. This is done by one step ahead out of sample prediction. The one step ahead out of sample prediction is done for the 500 observations at the end of the sample. To calculate the predictions a rolling forecast is used. This means that the sample that is used to do the one step ahead predictions is equally sized for all 500 predictions. Then tests are performed to evaluate the predictive power of the forecasts. The tests that are used to evaluate the predictions are: the dynamic quantile test, the Kupiec test and the Christoffersens test. The data that is used in the analysis are two stock indexes and one exchange rate index. What is concluded from the thesis is that the models perform good in general for the Stockholmsb ̈orsen data. For the First north data the 1% V aR produced too high risk predictions so the exceedance rate became too low. For the 5% V aR the predictions were more accurate. For the exchange rate data the predictions from the models were generally good as well.