Rough multifactor volatility for SPX and VIX options
Mathematical Finance
2023-11-15 v2
Abstract
We provide explicit small-time formulae for the at-the-money implied volatility, skew and curvature in a large class of models, including rough volatility models and their multi-factor versions. Our general setup encompasses both European options on a stock and VIX options, thereby providing new insights on their joint calibration. The tools used are essentially based on Malliavin calculus for Gaussian processes. We develop a detailed theoretical and numerical analysis of the two-factor rough Bergomi model and provide insights on the interplay between the different parameters for joint SPX-VIX smile calibration.
Cite
@article{arxiv.2112.14310,
title = {Rough multifactor volatility for SPX and VIX options},
author = {Antoine Jacquier and Aitor Muguruza and Alexandre Pannier},
journal= {arXiv preprint arXiv:2112.14310},
year = {2023}
}
Comments
33 pages. We added Remarks 2.2, 4.2, 4.3 and Lemma 4.7