用物理约束神经网络加速期权定价，无需标注数据。
DeepSVM: Learning Stochastic Volatility Models with Physics-Informed Deep Operator Networks
- 基于物理约束的深度算子网络，直接学习波动率模型解算器。
- 训练损失低至10⁻⁵，跨参数空间预测精度高。
- 适合量化金融从业者，尤其关注实时定价与无套利建模。
实时校准随机波动率模型（SVM）受限于需反复求解耦合偏微分方程（PDE）。本文提出DeepSVM，一种物理信息深度算子网络（PI-DeepONet），用于学习整个参数空间下赫斯顿模型的解算子。不同于传统数据驱动深度学习方法，DeepSVM无需标注训练数据，而是通过硬性约束设计，确保终端收益与静态无套利条件。此外，采用残差自适应精化（RAR）稳定高梯度区域的训练过程。整体上，DeepSVM实现最终训练损失为10⁻⁵，并在典型市场动态下精准预测期权价格。尽管定价准确，但其衍生品希腊值在平价（ATM）区域存在噪声，凸显物理信息算子学习中高阶正则化的必要性。
原文摘要 · Abstract (English)
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.
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