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：我们提出了一种新方法，用于生成与历史价格相符的多资产隐含波动率曲面序列。该方法结合了函数型数据分析与神经随机微分方程，并引入概率积分变换惩罚项以减少模型设定错误。研究表明，学习隐含波动率曲面与价格的联合动态可生成与历史特征一致的市场情景，且这些情景位于基本无静态套利的曲面子流形内。最后，我们证明使用模拟曲面进行Delta对冲所产生的损益分布与真实损益保持一致。