Recent general equilibrium models prescribe predictable dynamics in the volatility surfaces that are implied by observed option prices. In this paper, we investigate the predictability of surfaces, using extensive time series of implied volatilities from over-the-counter options on eight different currencies, quoted against the Euro. We examine implied volatility surfaces in the context of predictability through three different models, two that employ parametric specifications to describe the surface and one that decomposes it into latent statistical factors. All examined models are shown to (a) accurately describe the surfaces in-sample, and (b) produce forecasts that are superior to hard-to-beat benchmarks that ignore information about the shape of the surface, in medium- to long-term horizons. We show that these forecasts can support profitable volatility trading strategies in the absence of transaction costs. Comparing across competing models, our results suggest that parametric models, that allow for a more structured description of the surface, are more successful in terms of forecasts’ accuracy and significance of trading profits.