Paper: arXiv 2505.08623

Authors: Antoine Jacquier, Adriano Oliveri Orioles, Zan Zuric

Abstract

We propose a tractable extension of the rough Bergomi model, replacing the fractional Brownian motion with a generalised grey Brownian motion, which we show to be reminiscent of models with stochastic volatility of volatility. This extension breaks away from the log-Normal assumption of rough Bergomi, thereby making it a viable suggestion for the Equity Holy Grail – the joint SPX/VIX options calibration. For this new (class of) model(s), we provide semi-closed and asymptotic formulae for SPX and VIX options and show numerically its potential advantages as well as calibration results.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical extension of the rough Bergomi model, providing semi-closed and asymptotic formulae. It includes numerical results and calibration, demonstrating a good balance of theoretical depth and empirical application. The novelty lies in the generalized grey Brownian motion and its application to joint SPX/VIX options calibration.

Research Flowchart

  flowchart TD
    A[Research Goal: Extend Rough Bergomi for Joint SPX/VIX Calibration] --> B{Methodology: Introduce Generalized Grey Brownian Motion};
    B --> C[Model Development: Generalized Grey Bergomi (GGB) Model];
    C --> D{Computational Processes: Derivation of Semi-closed & Asymptotic Formulae};
    D --> E[Data/Inputs: SPX & VIX Options Data];
    E --> F[Validation & Calibration: Numerical Analysis & Calibration Results];
    F --> G[Key Outcomes: Tractable Model, Improved Calibration, Stochastic Volatility of Volatility Features];