Stochastic elasticity of vol-of-vol and pricing of variance swaps

Abstract

Implied volatility and implied vol-of-vol are two different sources of risk but the latter has been generally neglected. However, recent studies show the importance of both risk factors for investment strategies. The elasticity of vol-of-vol is focused on in this paper. We propose a revised Heston model reflecting the random nature of vol-of-vol and obtain pricing formulas of variance swaps for simple returns. We use a perturbation technique to transform the problem into a partial differential equation problem and then use the Green function and Fourier transform methods to derive explicitly a quasi-closed form approximation of the fair strike price. Subsequent result shows a comparison with the Heston result and the impact of the stochastic elasticity of vol-of-vol on the variance swap price.