Revisiting the long memory dynamics of implied-realized volatility relation: A new evidence from wavelet band spectrum regression

This paper revisits the fractional co-integrating relationship between ex-ante implied volatility and ex-post realized volatility. Previous studies on stock index options have found biases and inefficiencies in implied volatility as a forecast of future volatility. It is argued that the concept of corridor implied volatility (CIV) should be used instead of the popular model-free option-implied volatility (MFIV) when assessing the relation as the latter may introduce bias to the estimation. In addition, a new tool for the estimation of fractional co-integrating relation between implied and realized volatility based on wavelets, a wavelet band least squares (WBLS) uncovers that corridor implied volatility is an unbiased forecast of future volatility in the long run. The main advantage of WBLS in comparison to other methods is that it allows us to work conveniently with potentially non-stationary volatility due to the properties of wavelets and allows us to study the relation at different investment horizons. In the estimation, we use the S&P 500 and DAX monthly and biweekly option prices covering the recent financial crisis, and we conclude that the dependence comes solely from the lower frequencies of the spectra representing long horizons. The findings enable improvement of future volatility forecasts by discarding the bias coming from the short horizons.