Paper: arXiv 2604.25123

Authors: Ying Liao, Ankush Agarwal, Florian Bourgey

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper leverages advanced stochastic calculus, weak-approximation techniques, and Hermite polynomial expansions to derive closed-form solutions for complex VIX dynamics. It simultaneously maintains high empirical relevance by providing explicit calibration methodologies and practical software implementation for modern volatility models like rough Bergomi.

Research Flowchart

  flowchart TD
    A[Research Goal: Pricing VIX Options] --> B[Inputs: Forward Variance Models]
    B --> C[Methodology: Weak-Approximation Techniques]
    C --> D[Process: Derive Closed-Form Expansions]
    D --> E[Process: Apply Computable Correction Terms]
    E --> F[Outcome: Fast/Accurate Calibration & Model Validation]
    F --> G[Result: No Numerical Root-Finding Required]

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1 of 43 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.