High-frequency trading : statistical analysis, modelling and regulation.

Summary This thesis consists of two interrelated parts. In the first part, we empirically study the behavior of high-frequency traders on European financial markets. In the second part, we use the results obtained to build new multi-agent models. The main objective of these models is to provide regulators and trading platforms with innovative tools to implement microstructure relevant rules and to quantify the impact of various participants on market quality.In the first part, we perform two empirical studies on unique data provided by the French regulator. We have access to all orders and trades of CAC 40 assets, at the microsecond scale, with the identities of the actors involved. We begin by comparing the behavior of high-frequency traders to that of other players, particularly during periods of stress, in terms of liquidity provision and trading activity. We then deepen our analysis by focusing on liquidity consuming orders. We study their impact on the price formation process and their information content according to the different categories of flows: high-frequency traders, participants acting as clients and participants acting as principal.In the second part, we propose three multi-agent models. Using a Glosten-Milgrom approach, our first model constructs the entire order book (spread and volume available at each price) from the interactions between three types of agents: an informed agent, an uninformed agent and market makers. This model also allows us to develop a methodology for predicting the spread in case of a change in the price step and to quantify the value of the priority in the queue. In order to focus on an individual scale, we propose a second approach where the specific dynamics of the agents are modeled by nonlinear Hawkes-type processes that depend on the state of the order book. In this framework, we are able to compute several relevant microstructure indicators based on individual flows. In particular, it is possible to classify market makers according to their own contribution to volatility. Finally, we introduce a model where liquidity providers optimize their best bid and offer prices according to the profit they can generate and the inventory risk they face. We then theoretically and empirically highlight an important new relationship between inventory and volatility.