Modélisation du Carnet d'Ordres : Des Méthodes Statistiques aux Techniques d'Apprentissage Automatique

In today’s fast-paced financial markets, understanding the intricacies of trading mechanisms and price dynamics is essential for investors, regulators, and researchers alike. The Limit Order Book (LOB) serves as a central mechanism in these modern electronic markets, capturing the interactions between buyers and sellers. This thesis focuses on understanding the micro-dynamics of prices and order flow within LOBs, with the overarching goal of enhancing predictive modeling and simulation techniques utilised in financial analysis.The investigation begins by establishing a framework for defining significant price changes and proposing an optimal time scale for capturing meaningful information. To achieve this, we employ Principal Component Analysis to identify and establish "microstructure modes," which represent the most common flow-return patterns in the market. With these foundational insights, we develop a Vector Auto-Regressive (VAR) model aimed at predicting the next price change within the LOB. The calibration of this model demonstrates substantial predictive power, thereby contributing to the ongoing conversation regarding the potential for "endogenous liquidity crises" that can emerge from the interplay of different market dynamics.Building upon this analytical framework, we then explore self-attention mechanisms derived from machine learning to model the same phenomena. This modern approach allows us to assess the efficiency of a highly parameterized framework in capturing the dynamics of price changes and order flows.An additional focus of this thesis is the simulation of LOB time series using Recurrent Neural Networks (RNNs), which are well-suited for modeling sequential data. Initially, we address the trade-by-trade time scale, where we model the evolution of the first three levels of the LOB, optimising for accuracy in time-step dynamics. This detailed analysis enables us to evaluate our model's capacity to replicate stable empirical observations seen in real financial markets over extended periods. Subsequently, we extend our study to simulate the complete LOB at the tick-by-tick level, providing a nuanced understanding of market behaviour and interactions.Ultimately, this multi-faceted approach aims to significantly enhance our understanding of market microstructure while improving the predictive and generative capabilities of LOB models.