A empirical study of one-day risk prognosis models, using Value-at-Risk and three different GARCH-models

Abstract: This thesis assess three different conditional variance models from the GARCH family - GARCH(1,1), EGARCH(1,1) and GJR-GARCH(1,1) - and their accuracy in making one-day forecasts together with Value at Risk. The study is made on the daily returns of the OMX Stockholm 30 index between 2002-01-01 and 2010- 12-31. A five year in-sample set was used to estimate the model parameters and to make one-day VaR predictions at 90%, 95% and 99% confidence level the following year (out-of-sample). This process was run four times where the in- and out-of- sample were updated with one year. A total of four VaR forecasts was produced for each model and for each VaR level. Christoffersen’s three likelihood ratio tests were used to evaluate the models forecast accuracy. The results points toward GARCH(1,1) being the most accurate model, since the model was not rejected by any of the Christoffersen’s tests and at any VaR levels. However, limitations such as the number of observations used in the out-of-sample set, the number of model parameters to be estimated for each model and the assumed standard normally distributed innovations and return series may have had en effect on the result.