Paper: arXiv 2510.19126

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]