En empirisk studie av Value-at-Risk-prediktering med hjälp av GARCH-modeller

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This paper describes a study examining four different GARCH models AR(1)-GARCH(1,1), AR(1)-EGARCH(1,1), AR(1)-APGARCH(1,1) and AR(1)-GJR-GARCH(1,1), and their ability to predict future volatility and thereby providing more reliable estimates for Value-at-Risk. The study is based on daily observations for the return of the OMX Stockholm 30 Index, during the time period 31st December 1996 to 29th December 2006. The coefficients for these GARCH models have been estimated using a five-year rolling estimation window, with one-year lags, for five different in-sample-periods. These five in-sample-periods, and the coefficients given by them, have been used to generate five out-of-sample predictions for the volatility in each year. Using these volatility predictions, the daily Value-at-Risk has been calculated for confidence intervals of 90 percent, 95 percent, and 99 percent, respectively, during the time period between 1st January 2001 and 29th December 2006. Christoffersen??s test has then been applied to ensure that the models are reliable. When the four GARCH models are compared to each other, the results suggest that, for all confidence intervals, none of them is systematically superior to any of the other models. However, when looking a...