  This paper revisits the fractional cointegrating relationship between ex-ante
implied volatility and ex-post realized volatility. We argue that the concept
of corridor implied volatility (CIV) should be used instead of the popular
model-free option-implied volatility (MFIV) when assessing the fractional
cointegrating relation as the latter may introduce bias to the estimation. For
the realized volatility, we use recently proposed methods which are robust to
noise as well as jumps and interestingly we find that it does not affect the
implied-realized volatility relation. In addition, we develop a new tool for
the estimation of fractional cointegrating relation between implied and
realized volatility based on wavelets, a wavelet band least squares (WBLS). The
main advantage of WBLS in comparison to other frequency domain methods is that
it allows us to work conveniently with potentially non-stationary volatility
due to the properties of wavelets. We study the dynamics of the relationship in
the time-frequency domain with the wavelet coherence confirming that the
dependence comes solely from the lower frequencies of the spectra. Motivated by
this result we estimate the relationship only on this part of the spectra using
WBLS and compare our results to the fully modified narrow-band least squares
(FMNBLS) based on the Fourier frequencies. In the estimation, we use the S&P
500 and DAX monthly and bi-weekly option prices covering the recent financial
crisis and we conclude that in the long-run, volatility inferred from the
option prices using the corridor implied volatility (CIV) provides an unbiased
forecast of the realized volatility.
