Talk by Jules Delemotte, PhD student at CMAP, Ecole Polytechnique
Title: Smile dynamics and rough volatility
Abstract:
We investigate the dynamic properties of various stochastic, and notably rough, volatility
models, with an emphasis on the dynamics of implied volatilities. While recent literature
has extensively analyzed static properties, such as a model’s calibration power or the term
structure of at-the-money skews, dynamic features have received less attention. We focus
on the Skew-Stickiness Ratio (SSR), an industry-standard indicator of joint spot price and
implied volatility dynamics, pursuing the analysis of [Bergomi, Smile Dynamics IV, Risk,
2009] and extending it to rough volatility models. Using different numerical estimators, we
compare the behavior of the SSR generated by several models (not limited to the affine
framework) with the empirical market SSR estimated for the SPX Index. Interestingly, we
observe that different forward variance models—two-factor Bergomi, rough Bergomi, rough
Heston, Heston—calibrated as best as possible to the same SPX smile generate SSR that (i)
are close to one another, and (ii) display significant deviations from market data, failing to
reproduce the term structure observed for the empirical SSR. These observations suggest a
certain rigidity within the stochastic volatility family under consideration, and indicate that
rough volatility alone does not significantly alter the joint spot-implied volatility dynamics.
Joint work with Florian Bourgey and Stefano de Marco