Since the seminal model of Black, Scholes and Merton, the pricing and hedging of over-the-counter derivatives has been done almost exclusively by representing the market dynamics by a classical model which favours tractability so that important quantities such as prices and risk-management signals can be computed either in closed-form or with fast numerics. This approach made sense prior to the expansion of available data and development of more sophisticated computational models as well as hardware.

This thesis has one overarching aim - to develop novel approaches to pricing and hedging of derivatives which are fundamentally data driven. We develop machine learning methods for the full end-to-end pipeline of derivatives risk-management, from synthetic market data generation, to portfolio pricing and hedging strategy optimisation.
The main body of this thesis is split into three chapters. In the first chapter, we study profitable trading strategies called statistical arbitrage, and develop a method to "remove the drift" from a market simulator to eliminate any profitable trading strategies. This is of central importance to add robustness to hedging strategies learned under the market simulator. In the second chapter, we look further into synthetic data generation and explore two novel approaches. The first integrates the results from the previous chapter to develop a risk-neutral market simulator, whilst the second uses signatures to develop a market simulator for non-Markovian dynamics.
In the third chapter, we develop a recursive dynamic programming formulation of the hedging problem, through a non-linear, risk-averse Bellman equation. We then develop an actor-critic method to solving this, which we call deep Bellman hedging.