Robust pricing and hedging via neural SDEs

TL;DR

This paper introduces neural SDEs, a hybrid approach combining neural networks with classical SDE models, to provide robust derivative pricing, hedging strategies, and market scenario simulations, enhancing model reliability and interpretability.

Contribution

It proposes neural SDEs that integrate data-driven neural networks with traditional stochastic models, enabling robust calibration and scenario generation in finance.

Findings

Neural SDEs produce reliable bounds for derivative prices.

The approach allows calibration under both risk-neutral and real-world measures.

Numerical experiments validate the effectiveness of neural SDEs in finance.

Abstract

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.