Dynamics of limit orders book: statistical analysis, modelisation and prediction.

Summary This thesis is made of two connected parts, the rst one about limit order book modeling and the second one about tick value eects. In the rst part, we present our framework for Markovian order book modeling. The queuereactive model is rst introduced, in which we revise the traditional zero-intelligence approach by adding state dependency in the order arrival processes. An empirical study shows that this model is very realistic and reproduces many interesting microscopic features of the underlying asset such as the distribution of the order book. We also demonstrate that it can be used as an ecient market simulator, allowing for the assessment of complex placement tactics. We then extend the queue-reactive model to a general Markovian framework for order book modeling. Ergodicity conditions are discussed in details in this setting. Under some rather weak assumptions, we prove the convergence of the order book state towards an invariant distribution and that of the rescaled price process to a standard Brownian motion. In the second part of this thesis, we are interested in studying the role played by the tick value at both microscopic and macroscopic scales. First, an empirical study of the consequences of a tick value change is conducted using data from the 2014 Japanese tick size reduction pilot program. A prediction formula for the eects of a tick value change on the trading costs is derived and successfully tested. Then, an agent-based model is introduced in order to explain the relationships between market volume, price dynamics, bid-ask spread, tick value and the equilibrium order book state. In particular, we show that the bid-ask spread emerges naturally from the fact that orders placed too close to the ecient price have in general negative expected returns. We also nd that the bid-ask spread turns out to be the sum of the tick value and the intrinsic bid-ask spread, which corresponds to a hypothetical value of the bid-ask spread under innitesimal tick value.