Implied Volatility Expansions for VIX Options in Forward Variance Models

Ying Liao, Ankush Agarwal and Florian Bourgey

Papers from arXiv.org

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. 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.

Date: 2026-04
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