The Generalized Autoregressive Score (GAS), Exponential GAS (EGAS) and Asymmetric Exponential GAS (AEGAS) are new classes of volatility models that simultaneously account for jumps and asymmetry. Using these models, we estimate the dynamic pattern of the Nigeria All Share Index (ASI) from January 3, 2006 to July 22, 2014. Parameter estimates of the models were obtained using the Quasi Maximum Likelihood (QML) approach, and in-sample conditional volatility forecasts from each of the models were evaluated using the minimum loss function approach. Among the classical volatility models, the initial results detected IGARCH-t as the best model for predicting volatility in the ASI. However, in estimating the GAS variants, the Beta-t-EGARCH model proves to predict the volatility in the stock returns better than the IGARCH-t. The estimates could not improve further when the skewed version of the Student-t distribution was considered. We therefore recommend the GAS, EGAS and AEGAS family models in predicting jumps, outliers and asymmetry in financial time series modelling.