Realised Volatility Moments Implied by Asset Options

Abstract

For small values of correlation a method is given to de-correlate the instantaneous volatility from the price process in stochastic volatility models. The result of the de-correlation is that the implied volatility skew is rotated into a smile. Once the implied volatility skew has been “symmetrised”, moments of realised volatility are implied from the symmetrised asset option prices. The implied moments are subsequently used in a Gram-Charlier expansion of the density of realised volatility. The Gram-Charlier density provides approximate prices for options on realised volatility and other volatility derivatives.

This paper is available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4840162