A comparison of GARCH models for VaR estimation

In this paper the value at risk (VaR) forecasts are compared using three different GARCH models; ARCH(1), GARCH(1,1) and EGARCH(1,1). The implemented method is a one-day ahead out of sample forecast of the VaR. The forecasts are evaluated using the Kupiec test with a five percent significance level. The focus is on three different markets; commodities, equities and exchange rates. The goal of this thesis is to answer which of the models; ARCH(1), GARCH(1,1) and EGARCH(1,1) is best at forecasting the VaR for commodities, equities and exchange rates. Which assumed distribution for the conditional variance performs the best? Is the normal distribution or the Student-t a better option when forecasting VaR? The results shows that the ARCH(1) and EGARCH(1,1) model specifications are good options for forecasting the VaR for the chosen securities. These models give rise to a statistical significant forecast for the VaR with only one exception, the exchange rate between the SEK and USD. The worst performing model is the GARCH(1,1), which showed no significant results for any security. The normal distribution is the preferred conditional distribution assumption. In some securities the Student-t distribution shows a marginally better result, but the normal distribution is also a valid option in those cases.