Modeling and statistical analysis of price formation across scales, Market impact.

Summary The development of organized electronic markets puts constant pressure on academic research in finance. The price impact of a stock market transaction involving a large quantity of shares over a short period of time is a central topic. Controlling and monitoring the price impact is of great interest to practitioners, and its modeling has thus become a central focus of quantitative finance research. Historically, stochastic calculus has gradually been imposed in finance, under the implicit assumption that asset prices satisfy diffusive dynamics. But these hypotheses do not hold at the level of "price formation", i.e. when one considers the fine scales of market participants. New mathematical techniques derived from the statistics of point processes are therefore progressively imposed. The observables (processed price, middle price) appear as events taking place on a discrete network, the order book, and this at very short time scales (a few tens of milliseconds). The approach of prices seen as Brownian diffusions satisfying equilibrium conditions becomes rather a macroscopic description of complex phenomena arising from price formation. In the first chapter, we review the properties of electronic markets. We recall the limitations of diffusive models and introduce Hawkes processes. In particular, we review the research on the maket impact and present the progress of this thesis. In a second part, we introduce a new continuous time and discrete space impact model using Hawkes processes. We show that this model takes into account the microstructure of markets and is able to reproduce recent empirical results such as the concavity of the temporary impact. In the third chapter, we study the impact of a large volume of action on the price formation process at the daily scale and at a larger scale (several days after the execution). Furthermore, we use our model to highlight new stylized facts discovered in our database. In a fourth part, we focus on a non-parametric estimation method for a one-dimensional Hawkes process. This method relies on the link between the self-covariance function and the kernel of the Hawkes process. In particular, we study the performance of this estimator in the direction of the squared error on Sobolev spaces and on a certain class containing "very" smooth functions.