Precise asymptotics: robust stochastic volatility models
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.
Cite
@article{arxiv.1811.00267,
title = {Precise asymptotics: robust stochastic volatility models},
author = {Peter K. Friz and Paul Gassiat and Paolo Pigato},
journal= {arXiv preprint arXiv:1811.00267},
year = {2021}
}