No-Arbitrage Option Pricing with Neural SDEs

Phytides, Alexio

No-Arbitrage Option Pricing with Neural SDEs

Thesis / Dissertation

2023

Abstract

Neural stochastic differential equations (SDEs) represent a significant advancement in the field of machine learning by combining the power of neural networks and SDEs, two influential modelling approaches. SDEs are used to model systems that exhibit randomness or uncertainty and are defined by a set of differential equations that describe the evolution of the system over time, along with a random noise term. Neural SDEs extend this framework by using neural networks to model the SDE's drift and/or diffusion coefficients, resulting in a more flexible and powerful modelling approach. This dissertation delves into the use of neural SDEs for modelling the complex dynamics of asset price processes. Through a thorough examination of various training methodologies for neural SDEs, we aim to develop a more pragmatic approach to training these models, thereby advancing the understanding of neural SDEs and their potential for modelling financial systems. Through numerical experiments, we compare the performance of neural SDEs to well-established models, such as the Black-Scholes and CEV models, using European call option prices computed from neural SDE generated stock prices. The numerical experiment results suggest that neural SDEs are a promising tool for understanding the behaviour of complex, dynamic systems, and may offer improved accuracy and flexibility compared to traditional option pricing approaches. Overall, this work provides insight into the use of neural SDEs for modelling the intricacies of financial systems and other types of dynamic processes.

Keywords

Finance and Tax

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