  We present small-time implied volatility asymptotics for Realised Variance
(RV) and VIX options for a number of (rough) stochastic volatility models via
large deviations principle. We provide numerical results along with efficient
and robust numerical recipes to compute the rate function; the backbone of our
theoretical framework. Based on our results, we further develop approximation
schemes for the density of RV, which in turn allows to express the volatility
swap in close-form. Lastly, we investigate different constructions of
multi-factor models and how each of them affects the convexity of the implied
volatility smile. Interestingly, we identify the class of models that generate
non-linear smiles around-the-money.
