Vol-of-vol expansion for (rough) stochastic volatility models

We introduce an asymptotic small noise expansion, a so called vol-of-vol expansion, for potentially infinite dimensional and rough stochastic volatility models. Thereby we extend the scope of existing results for finite dimensional models and validate claims for infinite dimensional models. Furthermore we provide new, explicit (in the sense of non-recursive) representations of the so-called push-down Malliavin weights that utilizes a precise understanding of the terms of this expansion.