DeepSVM: Learning Stochastic Volatility Models with Physics-Informed Deep Operator Networks
Abstract
Real-time calibration of stochastic volatility models (SVMs) is computationally bottlenecked by the need to repeatedly solve coupled partial differential equations (PDEs). In this work, we propose DeepSVM, a physics-informed Deep Operator Network (PI-DeepONet) designed to learn the solution operator of the Heston model across its entire parameter space. Unlike standard data-driven deep learning (DL) approaches, DeepSVM requires no labelled training data. Rather, we employ a hard-constrained ansatz that enforces terminal payoffs and static no-arbitrage conditions by design. Furthermore, we use Residual-based Adaptive Refinement (RAR) to stabilize training in difficult regions subject to high gradients. Overall, DeepSVM achieves a final training loss of and predicts highly accurate option prices across a range of typical market dynamics. While pricing accuracy is high, we find that the model's derivatives (Greeks) exhibit noise in the at-the-money (ATM) regime, highlighting the specific need for higher-order regularization in physics-informed operator learning.
Cite
@article{arxiv.2512.07162,
title = {DeepSVM: Learning Stochastic Volatility Models with Physics-Informed Deep Operator Networks},
author = {Kieran A. Malandain and Selim Kalici and Hakob Chakhoyan},
journal= {arXiv preprint arXiv:2512.07162},
year = {2025}
}