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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 toshort-time and small noise formulae for option prices, using the framework[Bayer et al; A regularity structure for rough volatility; Math. Fin. 2020]. Weinvestigate here the fine structure of this expansion in large deviations andmoderate deviations regimes, together with consequences for implied volatility.We discuss computational aspects relevant for the practical application ofthese formulas. We specialize such expansions to prototypical rough volatilityexamples and discuss numerical evidence.

Short dated smile under Rough Volatility: asymptotics and numerics