  We consider rough stochastic volatility models where the driving noise of
volatility has fractional scaling, in the "rough" regime of Hurst parameter $H
< 1/2$. This regime recently attracted a lot of attention both from the
statistical and option pricing point of view. With focus on the latter, we
sharpen the large deviation results of Forde-Zhang (2017) in a way that allows
us to zoom-in around the money while maintaining full analytical tractability.
More precisely, this amounts to proving higher order moderate deviation
estimates, only recently introduced in the option pricing context. This in turn
allows us to push the applicability range of known at-the-money skew
approximation formulae from CLT type log-moneyness deviations of order
$t^{1/2}$ (recent works of Al\`{o}s, Le\'{o}n & Vives and Fukasawa) to the
wider moderate deviations regime.
