Title: Robust pricing and hedging via neural SDEs
Authors: Patryk Gierjatowicz - University of Edinburgh (United Kingdom)
Marc Sabate-Vidales - University of Edinburgh (United Kingdom)
David Siska - University of Edinburgh (United Kingdom) [presenting]
Lukasz Szpruch - University of Edinburgh (United Kingdom)
Zan Zuric - Imperial College London (United Kingdom)
Abstract: Modern data science techniques are opening the door to robust, data-driven model selection mechanisms. However, most machine learning models are ``black-boxes'' as individual parameters do not have a meaningful interpretation. In contrast, classical risk models based on stochastic differential equations (SDEs) with fixed parametrisation are well understood. Unfortunately, the risk of using an inadequate model is hard to detect and quantify. Instead of choosing a fixed parametrisation for the model SDE, we allow the drift and diffusion to be given by overparametrised neural networks. This allows one to find robust bounds for prices of derivatives and the corresponding hedging strategies. 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 the efficient use of neural SDEs and we validate our approach with numerical experiments using both market and synthetic data. The code used is available at Github.