Option-based forecasts of volatility: an empirical study in the DAX-index options market

Volatility estimation and forecasting are essential for both the pricing and the risk management of derivative securities. Volatility forecasting methods can be divided into option-based ones, which use prices of traded options in order to unlock volatility expectations, and time series volatility models, which use historical information in order to predict future volatility. Among option-based volatility forecasts, we distinguish between the 'model-dependent' Black-Scholes implied volatility and the 'model-free' implied volatility, proposed by Britten-Jones and Neuberger [Option prices, implied price processes and stochastic volatility. Journal of Finance 55: 839-66], that does not rely on a particular option pricing model. The aim of this paper is to investigate the unbiasedness and efficiency, with respect to past realised volatility, of the two option-based volatility forecasts. The comparison is pursued by using intra-daily data on the DAX-index options market. Our results suggest that Black-Scholes implied volatility subsumes all the information contained in past realised volatility and is a better predictor for future realised volatility than model-free implied volatility.