We start by a quick literature review (based on ) and an introduction of the square-root law, before moving to Hawkes’ point processes  and studying in depth the theory behind self-exciting point processes. We then reintroduce the multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level presented in . We try to rebuild the same multivariate Hawkes process and estimate the kernels of the Hawkes’ from the empirical conditional mean intensities provided by two different order books using two different techniques. We then provide a computation of the estimated market impact profile from the provided data and briefly discuss extended models.
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