Precise asymptotics: robust stochastic volatility models

TL;DR

This paper introduces a novel approach using regularity structures and Laplace methods on model spaces to derive precise short-time asymptotics for option prices in classical and rough stochastic volatility models.

Contribution

It develops a new methodology combining regularity structures with Laplace techniques to analyze stochastic volatility models, refining asymptotic results for option pricing.

Findings

Provides precise short-time asymptotics for European options

Refines large deviation asymptotics in rough volatility models

Generalizes classical path space asymptotic methods

Abstract

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.