Precise asymptotics: Robust stochastic volatility models

We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard short-time small noise formulae for option prices. Our main tool is the theory regularity structures, which we use in form [Bayer et al; A structure rough volatility, 2017]. In essence, implement Laplace method on space models (in sense Hairer), generalizes classical works Azencott Ben Arous path then Aida, Inahama--Kawabi space. When applied e.g. setting [Forde-Zhang, Asymptotics 2017], one obtains precise asymptotic European options refine known deviation asymptotics.