# Robust pricing and hedging via neural SDEs

arXiv: https://arxiv.org/abs/2007.04154 · HTML: https://mlsanity.com/paper/2007.04154/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2020.

## Built on by (most cited first, 22 of 22)

- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Efficient and Accurate Gradients for Neural SDEs](https://mlsanity.com/paper/2105.13493/) (2021)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Non-adversarial training of Neural SDEs with signature kernel scores](https://mlsanity.com/paper/2305.16274/) (2023)
- [Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer](https://mlsanity.com/paper/2201.13094/) (2022)
- [Generalization bounds for neural ordinary differential equations and deep residual networks](https://mlsanity.com/paper/2305.06648/) (2023)
- [Arbitrage-free neural-SDE market models](https://mlsanity.com/paper/2105.11053/) (2021)
- [Global universal approximation of functional input maps on weighted spaces](https://mlsanity.com/paper/2306.03303/) (2023)
- [Robust Risk-Aware Option Hedging](https://mlsanity.com/paper/2303.15216/) (2023)
- [FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs](https://mlsanity.com/paper/2303.00859/) (2023)
- [Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations](https://mlsanity.com/paper/2202.06637/) (2022)
- [Efficient Training of Neural Stochastic Differential Equations by Matching Finite Dimensional Distributions](https://mlsanity.com/paper/2410.03973/) (2024)
- [Risk-Neutral Market Simulation](https://mlsanity.com/paper/2202.13996/) (2022)
- [Deep Neural Networks Inspired by Differential Equations](https://mlsanity.com/paper/2510.09685/) (2025)
- [Efficient Neural SDE Training using Wiener-Space Cubature](https://mlsanity.com/paper/2502.12395/) (2025)
- [HGAN-SDEs: Learning Neural Stochastic Differential Equations with Hermite-Guided Adversarial Training](https://mlsanity.com/paper/2512.20272/) (2025)
- [Calibration of Derivative Pricing Models: a Multi-Agent Reinforcement Learning Perspective](https://mlsanity.com/paper/2203.06865/) (2022)
- [Sig-Splines: universal approximation and convex calibration of time series generative models](https://mlsanity.com/paper/2307.09767/) (2023)
- [Conditional Deep Levy Models for Exotic Derivatives: History-Aware Path Generation and P-Q Payoff Diagnostics](https://mlsanity.com/paper/2509.13374/) (2025)
- [Learning Manifold and Ito Dynamics with Branched Neural Rough Differential Equations](https://mlsanity.com/paper/2606.05272/) (2026)
- [NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes](https://mlsanity.com/paper/2607.14361/) (2026)
- [Structured Neural SDEs for Functional Calibration](https://mlsanity.com/paper/2609.34831/) (2026)

## Abstract (arXiv)

Mathematical modelling is ubiquitous in the financial industry and drives key decision processes. Any given model provides only a crude approximation to reality and the risk of using an inadequate model is hard to detect and quantify. By contrast, modern data science techniques are opening the door to more robust and data-driven model selection mechanisms. However, most machine learning models are "black-boxes" as individual parameters do not have meaningful interpretation. The aim of this paper is to combine the above approaches achieving the best of both worlds. Combining neural networks with risk models based on classical stochastic differential equations (SDEs), we find robust bounds for prices of derivatives and the corresponding hedging strategies while incorporating relevant market data. The resulting model called neural SDE is an instantiation of generative models and is closely linked with the theory of causal optimal transport. Neural SDEs allow consistent calibration under both the risk-neutral and the real-world measures. Thus the model can be used to simulate market scenarios needed for assessing risk profiles and hedging strategies. We develop and analyse novel algorithms needed for efficient use of neural SDEs. We validate our approach with numerical experiments using both local and stochastic volatility models.