Sam Cohen is an Associate Professor in the Mathematical Institute at the University of Oxford, and a Fellow of the Alan Turing Institute, where he leads the Machine Learning for Finance research theme. His research covers machine learning, reinforcement learning and optimal control theory, and stochastic analysis.
Modelling joint dynamics of liquid vanilla options is crucial for arbitrage-free pricing of illiquid derivatives and managing risks of option trade books. This paper develops a nonparametric model for the European options book respecting underlying financial constraints and while being practically implementable. We derive a state space for prices which are free from static (or model-independent) arbitrage and study the inference problem where a model is learnt from discrete time series data of stock and option prices. We use neural networks as function approximators for the drift and diffusion of the modelled SDE system, and impose constraints on the neural nets such that no-arbitrage conditions are preserved. In particular, we give methods to calibrate neural SDE models which are guaranteed to satisfy a set of linear inequalities. We validate our approach with numerical experiments using data generated from a Heston stochastic local volatility model.
Joint work with Christoph Reisinger, Sheng Wang.
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