An Efficient Calibration Framework for Volatility Derivatives under Rough Volatility with Jumps

ArXiv ID: 2510.19126 “View on arXiv”

Authors: Keyuan Wu, Tenghan Zhong, Yuxuan Ouyang

Abstract

We present a fast and robust calibration method for stochastic volatility models that admit Fourier-analytic transform-based pricing via characteristic functions. The design is structure-preserving: we keep the original pricing transform and (i) split the pricing formula into data-independent inte- grals and a market-dependent remainder; (ii) precompute those data-independent integrals with GPU acceleration; and (iii) approximate only the remaining, market-dependent pricing map with a small neural network. We instantiate the workflow on a rough volatility model with tempered-stable jumps tailored to power-type volatility derivatives and calibrate it to VIX options with a global-to-local search. We verify that a pure-jump rough volatility model adequately captures the VIX dynamics, consistent with prior empirical findings, and demonstrate that our calibration method achieves high accuracy and speed.

Keywords: Stochastic Volatility, Rough Volatility, Model Calibration, VIX Options, Fourier Pricing, Derivatives

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper features advanced mathematical modeling with rough volatility, tempered-stable Lévy processes, and Fourier transforms requiring complex numerical integration, indicating high math complexity. Empirically, it includes real-world VIX option data, calibration procedures, GPU acceleration, and neural network surrogates, demonstrating strong implementation and backtest readiness.

  flowchart TD
    A["Research Goal:<br/>Fast Calibration of<br/>Rough Volatility Models"] --> B["Methodology: Decomposition & Precomputation"]
    B --> C{"Structure-Preserving Design"}
    C --> D["Split Pricing Formula:<br/>Data-Independent Integrals"]
    C --> E["Market-Dependent Remainder"]
    D --> F["Precompute Integrals<br/>with GPU Acceleration"]
    E --> G["Approximate with<br/>Small Neural Network"]
    F --> H["Data Input:<br/>VIX Options Market Data"]
    G --> H
    H --> I["Calibration:<br/>Global-to-Local Search"]
    I --> J["Key Findings & Outcomes<br/>• High Accuracy & Speed<br/>• Pure-Jump Rough Model<br/>Captures VIX Dynamics<br/>• Efficient Framework for<br/>Volatility Derivatives"]