The aim of this paper is to compare the forecasting performance of competing volatility models, in order to capture the asymmetric effect in the volatility. We focus on examining the relative out-of-sample forecasting ability of the models (SETAR-TGARCH and SETAR-THSV), which contain the introduction of regimes based on thresholds in the mean equation and volatility equation, compared to the GARCH model and SV model. For each model, we consider two cases: Gaussian and t-Student measurement noise distribution. An important problem when evaluating the predictive ability of volatility models is that the “true” underlying process is not observable and thus a proxy must be defined for the unobservable volatility. To attain our proposal, the proxy volatility measure and the loss function must also be decided to ensure a correct ranking of models. Our empirical application suggests the following results: when time series include leverage effects on the mean, the introduction of threshold in the mean and variance equations produces more accurate predictions. If the leverage in the mean is not important, then the SVt is flexible enough to beat the threshold models.