The implied-realized volatility relation with jumps in underlying asset prices

Recent developments allow a nonparametric separation of the continuous sample path component and the jump component of realized volatility. The jump component has very different time series properties than the continuous component, and accounting for this allows improved forecasting of future realized volatility. We investigate the potential forecasting role of implied volatility backed out from option prices in the presence of these new separate realized volatility components. We show that implied volatility has incremental information relative to both the continuous and jump components of realized volatility when forecasting subsequently realized return volatility, and it appears to be an unbiased forecast. Furthermore, implied volatility has predictive power for future values of each component of realized volatility separately, showing in particular that even the jump component of realized volatility is, to some extent, predictable.