Short dated smile under Rough Volatility: asymptotics and numerics

TL;DR

This paper develops asymptotic formulas for option prices in rough volatility models, analyzing their behavior in short-time and small noise regimes, with implications for implied volatility and numerical methods.

Contribution

It introduces a new methodology for deriving precise asymptotics in rough volatility models, extending previous frameworks to include detailed deviation regimes and computational aspects.

Findings

Asymptotic expansions for option prices in rough volatility models

Analysis of large and moderate deviations regimes

Numerical evidence supporting the theoretical formulas

Abstract

In [Precise Asymptotics for Robust Stochastic Volatility Models; Ann. Appl. Probab. 2021] we introduce 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, using the framework [Bayer et al; A regularity structure for rough volatility; Math. Fin. 2020]. We investigate here the fine structure of this expansion in large deviations and moderate deviations regimes, together with consequences for implied volatility. We discuss computational aspects relevant for the practical application of these formulas. We specialize such expansions to prototypical rough volatility examples and discuss numerical evidence.