Hawkes model for price and trades high-frequency dynamics

By Emmanuel Bacry, Jean-François Muzy. 2013

212 citations recorded by the source corpus.

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 four 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 price microstructure (including random time arrival of price moves, discrete price grid, high-frequency mean reversion, correlation functions behaviour 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 empirically estimated from the empirical conditional mean intensities. We provide numerical examples, application to real data and comparisons to former approaches.

Subfields: Applied Mathematics, Artificial Intelligence, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/4b9af5f482296c561ca9ecd4a53c46aae6979aea

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Citations in the corpus

Hawkes Processes in Finance (2015, methodology): “1s Exp Constrained Section 5 [7] Bacry et al.”
HAWKES PROCESSES ON LARGE NETWORKS (2016, unknown): “…ﬁnance (order arrivals, see Bauwens-Hautsch [6], Hewlett [22], market microstructure see Bacry et al. [2] and market impact see Bacry-Muzy [4, 5]), ﬁnancial price modelling across scales (Bacry et al. [3], Jaisson-Rosenbaum [24]), social networks interactions (Blundell et al. [7],…”
Limit theorems for nearly unstable Hawkes processes (2013, background): “Finally, a time-varying μ is an easy way to reproduce seasonalities observed on the market, see [7] (however, for simplicity, we work in this paper with a constant μ > 0).”
The adaptive nature of liquidity taking in limit order books (2014, methodology): “As shown in [4], using as sign predictor an AR(p) model when p → ∞, the statistical model of equation (6) proposed in [11] is equivalent to the propagator model (see [1, 3]).”