{"ID":2831486,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.07162","arxiv_id":"2512.07162","title":"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 $10^{-5}$ 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.","short_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...","url_abs":"https://arxiv.org/abs/2512.07162","url_pdf":"https://arxiv.org/pdf/2512.07162v1","authors":"[\"Kieran A. Malandain\",\"Selim Kalici\",\"Hakob Chakhoyan\"]","published":"2025-12-08T04:53:23Z","proceeding":"q-fin.CP","tasks":"[\"q-fin.CP\",\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}