DeepSVM: Learning Stochastic Volatility Models with Physics-Informed Deep Operator Networks

TL;DR

DeepSVM introduces a physics-informed deep operator network that efficiently learns the solution operator of the Heston stochastic volatility model without labeled data, enabling real-time option pricing across various market conditions.

Contribution

The paper presents DeepSVM, a novel physics-informed deep operator network that learns the Heston model's solution operator without labeled data, improving computational efficiency and accuracy.

Findings

Achieves a training loss of 10^{-5}

Predicts option prices accurately across market dynamics

Greeks exhibit noise in the ATM regime, indicating need for higher-order regularization

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 $10^{-5}$ 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.