The statistical and economic relevance of out-of-sample forecasts of implied volatility surfaces of equity options

The implied volatility surface (IVS) is a mapping of implied volatilities of options as a function of the moneyness and time-to-maturity. Capturing and forecasting the dynamics of these surface can contribute to trading and hedging strategies, as it contains information about the expected market volatility. I propose both a two-step approach based on principal components analysis (PCA) and a one-step approach based on a state-space model. Exogenous variables are included at a later stage to improve the predictions. The most relevant factors and exogenous variables are selected by the least angle regressions (LARS) algorithm. There are three main findings. First, both of the approaches capture the predictability of the IVS of equity options in the information technology (IT) sector. The one-step approach is the best performing averaged over time for each individual equity option in terms of performance evaluation measures. Second, the consideration of exogenous variables improves the predictions of both approaches in terms of statistical performance. The expected inflation and interest rates are found to contribute the most to the prediction of the IVS of equity options. Third, when disregarding transaction costs, the one-step ahead forecasts of both approaches are able to produce positive returns for an ATM straddle trading strategy. However, when accounting for transaction costs, these potential profits disappear.