Implied Volatility Expansions for VIX Options in Forward Variance Models
Computational Finance
2026-05-26 v2 Mathematical Finance
Abstract
We develop closed-form expansions for the implied volatility of VIX options within the class of forward variance models. Our approach builds on weak-approximation techniques for VIX option prices and yields explicit implied volatility expansions with computable correction terms. The resulting formulas enable fast and accurate calibration without requiring numerical root-finding using option prices. We illustrate the performance of the proposed expansions in both standard and rough Bergomi-type models, as well as in mixed specifications, and demonstrate their accuracy through numerical experiments.
Cite
@article{arxiv.2604.25123,
title = {Implied Volatility Expansions for VIX Options in Forward Variance Models},
author = {Ying Liao and Ankush Agarwal and Florian Bourgey},
journal= {arXiv preprint arXiv:2604.25123},
year = {2026}
}