Realized Volatility Moments Implied by Options with Applications to the Pricing of Realized Volatility 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 `"symmetrized", moments of realized volatility are implied from the symmetrized asset option prices. The implied moments are subsequently used in a Gram-Charlier expansion of the density of realized volatility. The Gram-Charlier density provides approximate prices for options on realized volatility and other volatility derivatives.

Keywords: Volatility, options, implied volatility, stochastic volatility, volatility derivatives