FuNVol: multi-asset implied volatility market simulator using functional principal components and neural SDEs
提出一种结合函数数据分析与神经随机微分方程的方法，生成多资产隐含波动率曲面序列，使其忠实于历史价格且无静态套利，并验证了模拟曲面用于Delta对冲产生的损益分布与实际情况一致。
We introduce a new approach for generating sequences of implied volatility (IV) surfaces across multiple assets that are 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 realized P&Ls.