Realized Volatility Skewness and Kurtosis Implied by Index Option Prices

For nonzero but small values of correlation a method is given to de-correlate the instantaneous volatility from the price process in stochastic volatility models. Once the skew has been symmetrized in this manner, it is possible to imply moments of realized volatility from the index option prices in this de-correlated setting. The implied moments can subsequently be used for an Edgeworth expansion of the density of realized volatility. The density thus constructed supplies approximate prices of options on realized volatility