Taylor-Made Volatility Swaps

Abstract

Using little else than the mixing formula and Taylor expansions we show that the volatility swap strike is approximately the implied volatility corresponding to the strike where the vanna and vomma of a vanilla option is zero. As this result does not require any heavy numerical computations, and is valid for a large class of stochastic volatility models, it can be used for fast and model-free indicative pricing of volatility swaps.