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