Non-Markovian Modelling of Limit Order Books with Generative Adversarial Networks

Abstract

This thesis studies the use of Wasserstein GAN with Gradient Penalty and Temporal Attention augmented Bilinear Layers (TABL) to generate synthetic limit order book (LOB) data. The primary goal is to assess whether a non-Markovian conditioning of future snapshots on LOB history improves realism and mid-price movement prediction relative to a Markovian baseline. The proposed W-GAN models learn price dynamics implicitly from historical order flow, without relying on explicit mid-price movement labels. Results demonstrate that non-Markovian models consistently generate more realistic LOB snapshots and achieve higher F1 scores in mid-price movement classification than the baseline model. Among them, a history length n =30 performed the best in matching stylised facts and mid-price movements. They also incorporate LOB snapshots with empty queues in training, and learns to reproduce empty queues, but less frequently than in real data. Computational constraints required simplifying the model outputs, resulting in minor compromises to the quality of the generated samples. These findings highlight the benefits of non-Markovian conditioning in LOB generation and suggest promising directions for future research on model stability, scalability, and cross-asset generalisation.