A rough SABR formula
Mathematical Finance
2021-05-13 v1
Abstract
Following an approach originally suggested by Balland in the context of the SABR model, we derive an ODE that is satisfied by normalized volatility smiles for short maturities under a rough volatility extension of the SABR model that extends also the rough Bergomi model. We solve this ODE numerically and further present a very accurate approximation to the numerical solution that we dub the rough SABR formula.
Cite
@article{arxiv.2105.05359,
title = {A rough SABR formula},
author = {Masaaki Fukasawa and Jim Gatheral},
journal= {arXiv preprint arXiv:2105.05359},
year = {2021}
}