# FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs

arXiv: https://arxiv.org/abs/2303.00859 · HTML: https://mlsanity.com/paper/2303.00859/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 46 references that are in the map.
- First posted on arXiv 1 Mar 2023.

## Builds on (most cited first, 18 of 18)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Deep Hedging](https://mlsanity.com/paper/1802.03042/) (2018)
- [Deep Hedging of Derivatives Using Reinforcement Learning](https://mlsanity.com/paper/2103.16409/) (2021)
- [A generative adversarial network approach to calibration of local stochastic volatility models](https://mlsanity.com/paper/2005.02505/) (2020)
- [Deep Hedging: Learning to Simulate Equity Option Markets](https://mlsanity.com/paper/1911.01700/) (2019)
- [Robust pricing and hedging via neural SDEs](https://mlsanity.com/paper/2007.04154/) (2020)
- [Reinforcement Learning with Dynamic Convex Risk Measures](https://mlsanity.com/paper/2112.13414/) (2021)
- [Deep Smoothing of the Implied Volatility Surface](https://mlsanity.com/paper/1906.05065/) (2019)
- [Arbitrage-free neural-SDE market models](https://mlsanity.com/paper/2105.11053/) (2021)
- [Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders](https://mlsanity.com/paper/2108.04941/) (2021)
- [Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning](https://mlsanity.com/paper/2206.14666/) (2022)
- [Incorporating prior financial domain knowledge into neural networks for implied volatility surface prediction](https://mlsanity.com/paper/1904.12834/) (2019)
- [Online Adaptive Machine Learning Based Algorithm for Implied Volatility Surface Modeling](https://mlsanity.com/paper/1706.01833/) (2017)

## Built on by (most cited first, 6 of 6)

- [Non-adversarial training of Neural SDEs with signature kernel scores](https://mlsanity.com/paper/2305.16274/) (2023)
- [Generative modeling for time series via Schr"odinger bridge](https://mlsanity.com/paper/2304.05093/) (2023)
- [Efficient Training of Neural Stochastic Differential Equations by Matching Finite Dimensional Distributions](https://mlsanity.com/paper/2410.03973/) (2024)
- [Universal approximation property of neural stochastic differential equations](https://mlsanity.com/paper/2503.16696/) (2025)
- [Efficient Neural SDE Training using Wiener-Space Cubature](https://mlsanity.com/paper/2502.12395/) (2025)
- [Kullback-Leibler Barycentre of Stochastic Processes](https://mlsanity.com/paper/2407.04860/) (2024)

## Abstract (arXiv)

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.