Modelling microstructure noise with Hawkes processes

Abstract : Hawkes processes are used for modeling tick-by-tick variations of a single or of a pair of asset prices. For each asset, two counting processes (with stochastic intensities) are associated respectively with the positive and negative jumps of the price. We show that, by coupling these two intensities, one can reproduce high-frequencymean reversion structure that is characteristic of the microstructure noise. Moreover, in the case of two assets, by coupling the stochastic intensities corresponding to the positive (resp. negative) jumps of each asset, we are able to reproduce the Epps effect, i.e., the decorrelation of the increments at microscopic scales. At large scale our model becomes diffusive and converge towards a standard Brownian motion. Analytical closed-form formulae for the mean signature plot, the diffusive correlation matrix and the cross-asset correlation function at any time-scale are given. Empirical results are shown on futures Euro-Bund and Euro-Bobl high frequency data.
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Contributor : Jean-François Muzy <>
Submitted on : Wednesday, June 29, 2011 - 10:31:26 AM
Last modification on : Wednesday, September 4, 2019 - 1:52:03 PM


  • HAL Id : hal-00604490, version 1


Emmanuel Bacry, Sylvain Delattre, Marc Hoffmann, J.-F. Muzy. Modelling microstructure noise with Hawkes processes. ICASSP 2011 International Conference on acoustics, speech and signal processing. Session: Signal Processing Methods for Finance Applications, May 2011, Prague, Czech Republic. ⟨hal-00604490⟩



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