Modelling microstructure noise with Hawkes processes

Emmanuel Bacry (), Sylvain Delattre, Marc Hoffmann () and J.-F. Muzy ()
Additional contact information
Emmanuel Bacry: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Sylvain Delattre: LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique
Marc Hoffmann: LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées - UPEM - Université Paris-Est Marne-la-Vallée - BEZOUT - Fédération de Recherche Bézout - CNRS - Centre National de la Recherche Scientifique - UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12 - CNRS - Centre National de la Recherche Scientifique
J.-F. Muzy: SPE - Laboratoire « Sciences pour l’Environnement » (UMR CNRS 6134 SPE) - CNRS - Centre National de la Recherche Scientifique - Università di Corsica Pasquale Paoli [Université de Corse Pascal Paoli]

Post-Print from HAL

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.

Date: 2011-05-22
References: Add references at CitEc
Citations: View citations in EconPapers (2)

Published in ICASSP 2011 International Conference on acoustics, speech and signal processing. Session: Signal Processing Methods for Finance Applications, May 2011, Prague, Czech Republic

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00604490

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().