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"]

Cited References (14)

  1. Power-type derivatives for rough volatility with jumps (2020) — link
  2. Advanced model calibration on bitcoin options (2019) — link
  3. Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models (2019) — link
  4. Volatility of volatility is (also) rough (2019) — link
  5. Hybrid scheme for Brownian semistationary processes (2015) — link
  6. Volatility is rough (2014) — link
  7. Volatility Jumps (2011) — link
  8. A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code (2000) — link
and 6 more
  1. The Fourier-cosine method for option pricing revisited (2015)
  2. NORTHWESTERN UNIVERSITY Department of Electrical Engineering and Computer Science L BFGS B FORTRAN SUBROUTINES FOR LARGE SCALE BOUND CONSTRAINED OPTIMIZATION by (1994)
  3. Genetic Algorithms in Search, Optimization, and Learning (1989)
  4. Sample functions of stochastic processes with independent increments (1961)
  5. GPU-accelerated pricing with CuPy. High-precision quadrature executed on the GPU reduces a single price evaluation from seconds to milliseconds, enabling the generation of large synthetic datasets
  6. Parameter Sampling: Use Latin Hypercube Sampling to draw parameter vectors { θ i } Ni =1 from the joint distribution defined by the chosen bounds

0 of 14 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.