Heterosedasticity in returns may be explainable by trading volume. We use different volume variables, including surprise volume - i.e. unexpected above-avergae trading activity - which is derived from uncorrelated volume innovations. Assuming eakly exogenous volume, we extend the Lamoureux and Lastrapes (1990) model by an asymmetric GARCH in-mean specification following Golstein et al. (1993). Model estimation for the U.S. as well as six large equity markets shows that surprise volume superior model fit and helps to explain volatility persistence as well as excess kurtosis. Surprise volume reveals a significant positive market risk premium, asymmetry, and a surprise volume effect in conditional variance. The findings suggest that, e.g., a surprise volume shock (breakdown) - i.e. large (small) contemporaneous and small (large) lagged surprise volume - relates to increased (decreased) conditional market variance and return.