Short-time asymptotics for non self-similar stochastic volatility models

TL;DR

This paper establishes a short-time large deviation principle for non self-similar stochastic volatility models, enabling analysis of rough volatility models without strict self-similarity assumptions, impacting option pricing and implied volatility.

Contribution

It introduces a new LDP applicable to non self-similar Volterra-based volatility models, broadening the scope of rough volatility analysis.

Findings

Derived implications for short-maturity European option prices

Analyzed implied volatility surfaces and skews

Provided simulation results for fOU models

Abstract

We provide a short-time large deviation principle (LDP) for stochastic volatility models, where the volatility is expressed as a function of a Volterra process. This LDP does not require strict self-similarity assumptions on the Volterra process. For this reason, we are able to apply such an LDP to two notable examples of non self-similar rough volatility models: models where the volatility is given as a function of a log-modulated fractional Brownian motion [Bayer et al., Log-modulated rough stochastic volatility models. SIAM J. Financ. Math, 2021, 12(3), 1257-1284], and models where it is given as a function of a fractional Ornstein-Uhlenbeck (fOU) process [Gatheral et al., Volatility is rough. Quant. Finance, 2018, 18(6), 933-949]. In both cases we derive consequences for short-maturity European option prices, implied volatility surfaces and implied volatility skew. In the fOU case we also discuss moderate deviations pricing and simulation results.