Stochastic modeling of order books.

Summary This thesis studies some aspects of stochastic modeling of order books. In the first part, we analyze a model in which the order arrival times are Poissonian independent. We show that the order book is stable (in the sense of Markov chains) and that it converges to its stationary distribution exponentially fast. We deduce that the price generated in this framework converges to a Brownian motion at large time scales. We illustrate the results numerically and compare them to market data, highlighting the successes of the model and its limitations. In a second part, we generalize the results to a framework where arrival times are governed by self- and mutually-existing processes, under assumptions about the memory of these processes. The last part is more applied and deals with the identification of a realistic multivariate model from the order flows. We detail two approaches: the first one by likelihood maximization and the second one from the covariance density, and succeed in having a remarkable agreement with the data. We apply the estimated model to two concrete algorithmic trading problems, namely the measurement of the execution probability and the cost of a limit order.