Refined expansions of the skew-stickiness ratio in stochastic volatility models

Abstract

Building on the celebrated Bergomi–Guyon expansion, we derive next-to-leading order expansions in the volatility-of-volatility parameter for the Skew-Stickiness Ratio—an indicator of implied volatility dynamics—within a general class of forward variance models, thus pursuing the seminal work of Bergomi on explicit approximation formulas for the SSR. We demonstrate the accuracy of these expansions using parameters calibrated to the SPX market across several models, including the two-factor Bergomi, rough Bergomi, Heston, and rough Heston models.