Implied Volatility Expansions for VIX Options in Forward Variance Models

TL;DR

This paper introduces explicit, fast-to-compute implied volatility expansions for VIX options in forward variance models, improving calibration efficiency and accuracy.

Contribution

It provides novel closed-form implied volatility expansions using weak-approximation techniques, applicable to various forward variance models.

Findings

Expansions are accurate in standard and rough Bergomi models.

Calibration is faster without numerical root-finding.

Numerical experiments confirm the effectiveness of the expansions.

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.