Modeling of the price microstructure and applications of stochastic control to algorithmic trading.

Abstract : In this thesis, we take care of the modelling of the price of assets in the limit order book and of the application of the techniques of the optimal control in the algorithmic trading, in particular of market making. For assets with small tick, we develop an algorithm of market making in a book where the arrivals of order follow a Poisson law with average which decreases exponentially with the distance of the order from the mid-price. Thanks to techniques of asymptotic developments, we obtain explicit results for a very wide class of models, for which we suppose to know only the first two moments. For assets with large tick, we propose a new model based on a semi-Markov process, thanks to which we are able to replicate some stylized facts as the noise mean-reversion, the large-scale Brownian behavior, and the dependence of the variance estimator on the sampling frequency. In this environment, we describe an algorithm of market making using techniques of optimal control and asymptotic development, amazingly reducing the numerical part. Finally, we improve the previous model by using VLMCs (Variable length Markov chains), which allow to describe the long memory of the price, and, that, even if losing explicit formulae, allow to obtain interesting applications in the algorithmic trading.
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Pietro Fodra. Modeling of the price microstructure and applications of stochastic control to algorithmic trading.. Computational Finance [q-fin.CP]. Université Paris 7 - Diderot, 2015. English. ⟨tel-01161734⟩

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