Here, we introduce a new approach for generating sequences of implied volatility (IV) surfaces across multiple assets that is faithful to historical prices. We do so using a combination of functional data analysis and neural stochastic differential equations (SDEs) combined with a probability integral transform penalty to reduce model misspecification. We demonstrate that learning the joint dynamics of IV surfaces and prices produces market scenarios that are consistent with historical features and lie within the sub-manifold of surfaces that are essentially free of static arbitrage. Finally, we demonstrate that delta hedging using the simulated surfaces generates profit and loss (P&L) distributions that are consistent with realised P&Ls.

翻译：本文提出一种新的方法，用于生成跨多个资产的隐含波动率（IV）曲面序列，该序列忠实于历史价格数据。我们结合函数数据分析与神经随机微分方程（SDEs），并引入概率积分变换惩罚项以减少模型设定偏差。研究证明，通过学习IV曲面与价格的联合动态特性，所生成的市场场景与历史特征保持一致，且位于本质上无静态套利的曲面子流形内。最后，我们证实，利用模拟曲面进行Delta对冲产生的损益（P&L）分布与已实现损益分布一致。