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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.

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File URL: http://arxiv.org/pdf/1101.3422
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Paper provided by arXiv.org in its series Papers with number 1101.3422.

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Date of creation: Jan 2011
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Handle: RePEc:arx:papers:1101.3422

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References

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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. Mark Podolskij & Mathias Vetter, 2007. "Estimation of Volatility Functionals in the Simultaneous Presence of Microstructure Noise and Jumps," CREATES Research Papers 2007-27, School of Economics and Management, University of Aarhus.
  4. 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, School of Economics and Management, University of Aarhus.
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Cited by:
  1. Toke, Ioane Muni & Pomponio, Fabrizio, 2012. "Modelling trades-through in a limit order book using hawkes processes," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 6(22), pages 1-23.
  2. Olivier Gu\'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Science & Finance (CFM) working paper archive 1106.3279, Science & Finance, Capital Fund Management, revised Jul 2012.
  3. Toke, Ioane Muni & Pomponio, Fabrizio, 2011. "Modelling trades-through in a limited order book using Hawkes processes," Economics Discussion Papers 2011-32, Kiel Institute for the World Economy.
  4. Pietro Fodra & Huyen Pham, 2013. "High frequency trading in a Markov renewal model," Working Papers hal-00867113, HAL.
  5. Ban Zheng & Fran\c{c}ois Roueff & Fr\'ed\'eric Abergel, 2013. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Science & Finance (CFM) working paper archive 1301.5007, Science & Finance, Capital Fund Management, revised Feb 2014.
  6. Bacry, E. & Delattre, S. & Hoffmann, M. & Muzy, J.F., 2013. "Some limit theorems for Hawkes processes and application to financial statistics," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2475-2499.
  7. Vladimir Filimonov & Didier Sornette, 2013. "Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data," Science & Finance (CFM) working paper archive 1308.6756, Science & Finance, Capital Fund Management, revised Nov 2013.
  8. E. Bacry & J. F Muzy, 2013. "Hawkes model for price and trades high-frequency dynamics," Science & Finance (CFM) working paper archive 1301.1135, Science & Finance, Capital Fund Management.
  9. Thibault Jaisson, 2014. "Market impact as anticipation of the order flow imbalance," Science & Finance (CFM) working paper archive 1402.1288, Science & Finance, Capital Fund Management.
  10. Pietro Fodra & Huy\^en Pham, 2013. "High frequency trading in a Markov renewal model," Science & Finance (CFM) working paper archive 1310.1756, Science & Finance, Capital Fund Management.
  11. Aymen Jedidi & Frédéric Abergel, 2013. "Stability and price scaling limit of a Hawkes-process based order book model," Working Papers hal-00821607, HAL.
  12. Aim\'e Lachapelle & Jean-Michel Lasry & Charles-Albert Lehalle & Pierre-Louis Lions, 2013. "Efficiency of the Price Formation Process in Presence of High Frequency Participants: a Mean Field Game analysis," Science & Finance (CFM) working paper archive 1305.6323, Science & Finance, Capital Fund Management, revised Mar 2014.
  13. Giacomo Bormetti & Lucio Maria Calcagnile & Michele Treccani & Fulvio Corsi & Stefano Marmi & Fabrizio Lillo, 2013. "Modelling systemic price cojumps with Hawkes factor models," Science & Finance (CFM) working paper archive 1301.6141, Science & Finance, Capital Fund Management, revised Mar 2013.
  14. Guéant, Olivier & Lehalle, Charles-Albert & Tapia, Joaquin Fernandez, 2011. "Optimal Portfolio Liquidation with Limit Orders," Economics Papers from University Paris Dauphine 123456789/7391, Paris Dauphine University.
  15. Thibault Jaisson & Mathieu Rosenbaum, 2013. "Limit theorems for nearly unstable Hawkes processes," Science & Finance (CFM) working paper archive 1310.2033, Science & Finance, Capital Fund Management.
  16. Ioane Muni Toke & Fabrizio Pomponio, 2012. "Modelling Trades-Through in a Limit Order Book Using Hawkes Processes," Post-Print hal-00745554, HAL.
  17. Ban Zheng & François Roueff & Frédéric Abergel, 2013. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Working Papers hal-00777941, HAL.
  18. Wen Cao & Clifford Hurvich & Philippe Soulier, 2012. "Drift in transcation-level asset price models," Working Papers hal-00756372, HAL.
  19. Behzad Mehrdad & Lingjiong Zhu, 2014. "On the Hawkes Process with Different Exciting Functions," Science & Finance (CFM) working paper archive 1403.0994, Science & Finance, Capital Fund Management.
  20. Guéant, Olivier & Lehalle, Charles-Albert & Tapia, Joaquin Fernandez, 2011. "Dealing with the Inventory Risk," Economics Papers from University Paris Dauphine 123456789/7390, Paris Dauphine University.
  21. Geon Ho Choe & Kyungsub Lee, 2013. "Conditional correlation in asset return and GARCH intensity model," Science & Finance (CFM) working paper archive 1311.4977, Science & Finance, Capital Fund Management.
  22. Olivier Gu\'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Dealing with the Inventory Risk. A solution to the market making problem," Science & Finance (CFM) working paper archive 1105.3115, Science & Finance, Capital Fund Management, revised Aug 2012.
  23. Emmanuel Bacry & Jean-Francois Muzy, 2014. "Second order statistics characterization of Hawkes processes and non-parametric estimation," Science & Finance (CFM) working paper archive 1401.0903, Science & Finance, Capital Fund Management.

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