2013/01/07 by Emmanuel Bacry, Bacry, E., Jean–François Muzy +1 · 5 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Data Analysis #Diffusion and Search Dynamics #FOS: Economics and business #FOS: Physical sciences #Point processes and geometric inequalities #Statistics and Probability (physics.data-an) #Trading and Market Microstructure (q-fin.TR)
paper · pdf · doi:10.48550/arxiv.1301.1135
openalex publication_date 2013/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with respectively the trade arrival self-excitation, the price changes mean reversion the impact of trade arrivals on price variations and the feedback of price changes on trading activity. It allows one to account for both stylized facts of market prices microstructure (including random time arrival of price moves, discrete price grid, high frequency mean reversion, correlation functions behavior at various time scales) and the stylized facts of market impact (mainly the concave-square-root-like/relaxation characteristic shape of the market impact of a meta-order). Moreover, it allows one to estimate the entire market impact profile from anonymous market data. We show that these kernels can be estimated from the empirical conditional mean intensities. We provide numerical examples, application to real data and comparisons to former approaches.