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

TL;DR

This paper develops an asymptotic vol-of-vol expansion for infinite-dimensional and rough stochastic volatility models, extending previous finite-dimensional results and providing explicit representations of Malliavin weights.

Contribution

It introduces a novel asymptotic expansion for rough stochastic volatility models and offers explicit formulas for Malliavin weights, broadening the scope of existing methods.

Findings

Validates the expansion for infinite-dimensional models

Provides explicit, non-recursive formulas for Malliavin weights

Extends results from finite to infinite-dimensional models

Abstract

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.