  In [Precise Asymptotics for Robust Stochastic Volatility Models; Ann. Appl.
Probab. 2021] we introduce a new methodology to analyze large classes of
(classical and rough) stochastic volatility models, with special regard to
short-time and small noise formulae for option prices, using the framework
[Bayer et al; A regularity structure for rough volatility; Math. Fin. 2020]. We
investigate here the fine structure of this expansion in large deviations and
moderate deviations regimes, together with consequences for implied volatility.
We discuss computational aspects relevant for the practical application of
these formulas. We specialize such expansions to prototypical rough volatility
examples and discuss numerical evidence.
