Controle Optimal Dans Des Carnets D’ordres Limites Optimal Control in Limit Order Books

We propose a quantitative approach to some high frequency trading problematics. We are interested in several aspects of this field, from minimizing indirect trading costs to market making, and more generally in profit maximization strategies over a finite time horizon. We build an original framework that reflects specificities of high frequency trading, and especially the distinction between passive and active trading, thanks to mixed stochastic control methods. We carefully model high fequency market phenomena, and for each of them we propose calibration methods that are compatible with practical constraints of algorithmic trading. In chapter 3, we review the litterature on quantitative methods for high frequency trading. Firstly, we are interested in market impact and best execution problems modelling. Secondly, we provide an overview of profit-seeking high frequency trading strategies documented in academic litterature. In chapter 4, we propose a simple model for non-linear market impact, which reflects general properties of indirect trading costs. We study the case of an investor that wants to unwind their portfolio, and provide a strategy that maximizes the revenue of this sale. We numerically solve the corresponding impulse control problem, using a numerical whose convergence is proven, and we study the behaviour and performance of the strategy. In chapter 5, we build a model for a standard market microstructure, as encountered on european stocks for example, and we develop the statistical methods to calibrate the model. In this context, we consider a mixed market making strategy, where the investor can both provide and take liquidity in the market. We solve the problem of maximizing the profit using mixed stochastic control methods, that we solve numerically with a numerical scheme whose convergence is proven. We also provide a detailled performance analysis. In chapter 6, we build a model for an exotic market microstructure, as encountered on interest rates for example, and we show how this model can be calibrated. In this case again, we consider a mixed market making strategy, that we study by means of mixed stochastic control, and that we solve numerically. In this context, we introduce a central tool for industrial application of high frequency trading that allows us to use predictive information on short term evolution of price. Finally, we provide a performance analysis for this strategy, and we show how to modify the model to cover the costs optimization problem as well. te l-0 07 78 45 8, v er si on 2 23 J un 2 01 3