In this thesis we use the GARCH(1,1) and GJR-GARCH(1,1) models to estimate the conditional variance for five equities from the OMX Nasdaq Stockholm (OMXS) stock exchange. We predict 95% and 99% Value-at-Risk (VaR) using one-day ahead forecasts, under three different error distribution assumptions, the Normal, Student’s t and the General Error Distribution. A 500 observations rolling forecast-window is used on the dataset of daily returns from 2007 to 2014. The empirical size VaR is evaluated using the Kupiec’s test of unconditional coverage and Christoffersen’s test of independence in order to provide the most statistically fit model. The results are ultimately filtered to correspond with the Basel (II) Accord Penalty Zones to present the preferred models. The study finds that the GARCH(1,1) is the preferred model when predicting the 99% VaR under varying distribution assumptions.