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Modeling microstructure noise with mutually exciting point processes

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  • E. Bacry
  • S. Delattre
  • M. Hoffmann
  • J. F. Muzy

Abstract

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on marked point processes and relies on linear self and mutually exciting stochastic intensities as introduced by Hawkes. We associate a counting process with the positive and negative jumps of an asset price. By coupling suitably the stochastic intensities of upward and downward changes of prices for several assets simultaneously, we can reproduce microstructure noise (i.e. strong microscopic mean reversion at the level of seconds to a few minutes) and the Epps effect (i.e. the decorrelation of the increments in microscopic scales) while preserving a standard Brownian diffusion behaviour on large scales. More effectively, we obtain analytical closed-form formulae for the mean signature plot and the correlation of two price increments that enable to track across scales the effect of the mean-reversion up to the diffusive limit of the model. We show that the theoretical results are consistent with empirical fits on futures Euro-Bund and Euro-Bobl in several situations.

Suggested Citation

  • E. Bacry & S. Delattre & M. Hoffmann & J. F. Muzy, 2011. "Modeling microstructure noise with mutually exciting point processes," Papers 1101.3422, arXiv.org.
  • Handle: RePEc:arx:papers:1101.3422
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    1. Francis X. Diebold & Georg H. Strasser, 2008. "On the Correlation Structure of Microstructure Noise in Theory and Practice," PIER Working Paper Archive 08-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    2. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Discussion Papers (ECON - Département des Sciences Economiques) 2006039, Université catholique de Louvain, Département des Sciences Economiques.
    3. Jean Jacod & Yingying Li & Per A. Mykland & Mark Podolskij & Mathias Vetter, 2007. "Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9," CREATES Research Papers 2007-43, Department of Economics and Business Economics, Aarhus University.
    4. Vetter, Mathias & Podolskij, Mark, 2006. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," Technical Reports 2006,51, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
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