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：在本文中，我们介绍了一种新方法，利用函数数据分析和神经随机微分方程结合概率积分变换罚项来生成跨多个资产的隐含波动率（IV）曲面序列，以忠实于历史价格。我们证明了学习IV曲面和价格的联合动态会产生与历史特征一致的市场情景，并且在实质上没有静态套利的曲面的子流形内。最后，我们证明利用模拟的曲面进行三角套利可产生与实现P＆L一致的获利和损失（P&L）分布。