We specify a class of non-linear and non-Gaussian models for which we estimate and forecast the conditional distributions with daily frequency. We use these forecasts to calculate VaR measures for three different equity markets (US, GB and Japan). These forecasts are evaluated on the basis of different statistical performance measures as well as on the basis of their economic costs that go along with the forecasted capital requirements. The results indicate that different performance measures generate different rankings of the models even within one financial market. We also find that for the three markets the improvement in the forecast by non-linear models over linear ones is negligible, while non-gaussian models significantly dominate the gaussian models. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"