Assessing the information content of option-based volatility forecasts using fuzzy regression methods

Volatility is a key variable for portfolio selection models, option pricing models and risk management techniques. Volatility can be estimated and forecasted by using either historical information or option prices. The present paper focuses on option-based volatility forecasts for three main reasons. First, for the forward looking nature of option-based forecasts (as opposed to the backward looking nature of historical information); second, for the average superiority, documented in the literature, of option-based estimates in forecasting future realized volatility; third, for the widespread use of option prices in the computation of the most important market volatility indexes (see e.g. the VIX index for the Chicago Board Options Exchange). The aim of this paper is to assess the information content on future realised volatility of different option-based volatility forecasts, through the use of fuzzy regression methods. The latter methods offer a suitable tool to handle both imprecision in measurements and fuzziness of the relationship among variables. Therefore, they are particularly useful for volatility forecasting, since the variable of interest (realised volatility) is unobservable and a proxy for it is used. Moreover, measurement errors in both realised volatility and volatility forecasts may affect the regression results. Fuzzy regression methods have not yet been used in volatility forecasting. Our case study is based on intra-daily data on the DAX-index options market.