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. In this talk, we will consider 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 volatility model, and with observed market data.

Bio: Sam Cohen is a mathematician based at the Mathematical Institute in Oxford, and at the Alan Turing Institute in London. He obtained his PhD in 2011 at the University of Adelaide, under the supervision of Robert Elliott. He is interested in the interaction between statistical learning, decision making and modelling, with particular applications in finance and economics.