FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs
This work addresses the need for accurate market simulators in quantitative finance, offering a novel method for risk management and derivative pricing, though it is incremental in applying existing techniques to a specific domain.
The paper tackles the problem of generating realistic implied volatility surfaces for multiple assets by combining functional data analysis with neural stochastic differential equations, achieving simulated surfaces that are free of static arbitrage and produce delta-hedging P&L distributions consistent with real data.
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.