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Modelling microstructure noise with Hawkes processes

Author

Listed:
  • Emmanuel Bacry

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - 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 - Sciences pour l'environnement - UPP - Université Pascal Paoli - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & J.-F. Muzy, 2011. "Modelling microstructure noise with Hawkes processes," Post-Print hal-00604490, HAL.
    • Handle: RePEc:hal:journl:hal-00604490
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    Cited by:

    1. Holley, Elizabeth A. & Mitcham, Carl, 2016. "The Pebble Mine Dialogue: A case study in public engagement and the social license to operate," Resources Policy, Elsevier, vol. 47(C), pages 18-27.
    2. Tang, H.S. & Kraatz, S. & Qu, K. & Chen, G.Q. & Aboobaker, N. & Jiang, C.B., 2014. "High-resolution survey of tidal energy towards power generation and influence of sea-level-rise: A case study at coast of New Jersey, USA," Renewable and Sustainable Energy Reviews, Elsevier, vol. 32(C), pages 960-982.

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