We compare the predictive ability and economic value of implied, realized, and GARCH volatility models for 13 equity indices from 10 countries. Model ranking is similar across countries, but varies with the forecast horizon. At the daily horizon, the Heterogeneous Autoregressive model offers the most accurate predictions, whereas an implied volatility model that corrects for the volatility risk premium is superior at the monthly horizon. Widely used GARCH models have inferior performance in almost all cases considered. All methods perform significantly worse over the 2008–09 crisis period. Finally, implied volatility offers significant improvements against historical methods for international portfolio diversification. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 36:1164–1193, 2016