Journal of Mathematics and Modeling in Finance

Physics-Informed Neural Networks for Calibration of Rough Fractional Stochastic Volatility Models

Articles in Press

Document Type : Research Article

Author

Amirali Ghajari

Islamic Azad University - Central Tehran Branch, Tehran, Iran.

10.22054/jmmf.2026.94451.1310
Abstract
The calibration of stochastic volatility models is a fundamental inverse problem in quantitative finance, critical for accurate option pricing and risk management. While traditional calibration methods often struggle with the non-Markovian nature and high dimensionality of rough volatility models, recent advances in machine learning offer new pathways. This paper introduces a computational framework that employs Physics-Informed Neural Networks (PINNs) to solve the inverse problem of calibrating the rough fractional stochastic volatility (RFSV) model. We derive the governing fractional partial differential equation (fPDE) for the characteristic function of the log-price rigorously, via a multi-factor Markovian lift of the underlying Volterra process to which the classical Feynman-Kac theorem applies directly, and we make explicit the further approximation used to reduce the resulting high-dimensional Kolmogorov equation to the fractional-in-time equation enforced by the PINN. We embed this fPDE into the loss function of a characteristic-function network, and connect it to observed option prices through an explicit, non-trainable Fourier inversion bridge, so that the physics loss and the data loss act consistently on the same underlying network rather than on two unrelated objects. We also give a decomposed convergence result that separates neural approximation, Grünwald-Letnikov truncation and discretization, and optimization error, and we show that the fractional-derivative weights remain differentiable in the Hurst parameter during training. Through numerical experiments on synthetic and S&P 500 market data, reported over multiple random initializations with confidence intervals and significance tests, we demonstrate that the proposed PINN-based approach achieves superior accuracy and robustness in recovering the Hurst parameter and the volatility of volatility compared to conventional Monte-Carlo-based calibration, at substantially lower amortized computational cost.

Keywords

Physics-Informed Neural Networks
Rough Volatility
Fractional Brownian Motion
Calibration
Option Pricing
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Journal of Mathematics and Modeling in Finance

Articles in Press, Accepted Manuscript
Available Online from 15 September 2026

  • Receive Date 20 July 2026
  • Revise Date 12 September 2026
  • Accept Date 14 September 2026

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