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A Fokker-Planck description for the queue dynamics of large tick stocks

Author

Listed:
  • A. Gareche
  • G. Disdier
  • J. Kockelkoren
  • J. -P. Bouchaud

Abstract

Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation, that explicitly includes state dependence, i.e. the fact that the drift and diffusion depends on the volume present on both sides of the spread. "Jump" events, corresponding to sudden changes of the best limit price, must also be included as birth-death terms in the Fokker-Planck equation. All quantities involved in the equation can be calibrated using high-frequency data on best quotes. One of our central finding is the the dynamical process is approximately scale invariant, i.e., the only relevant variable is the ratio of the current volume in the queue to its average value. While the latter shows intraday seasonalities and strong variability across stocks and time periods, the dynamics of the rescaled volumes is universal. In terms of rescaled volumes, we found that the drift has a complex two-dimensional structure, which is a sum of a gradient contribution and a rotational contribution, both stable across stocks and time. This drift term is entirely responsible for the dynamical correlations between the ask queue and the bid queue.

Suggested Citation

  • A. Gareche & G. Disdier & J. Kockelkoren & J. -P. Bouchaud, 2013. "A Fokker-Planck description for the queue dynamics of large tick stocks," Papers 1304.6819, arXiv.org.
  • Handle: RePEc:arx:papers:1304.6819
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    File URL: http://arxiv.org/pdf/1304.6819
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    References listed on IDEAS

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    1. Avellaneda, Marco & Reed, Josh & Stoikov, Sasha, 2011. "Forecasting prices from level-I quotes in the presence of hidden liquidity," Algorithmic Finance, IOS Press, vol. 1(1), pages 35-43.
    2. Ioanid Rosu, 2009. "A Dynamic Model of the Limit Order Book," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4601-4641, November.
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    Citations

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    Cited by:

    1. Julius Bonart & Martin Gould, 2015. "Latency and liquidity provision in a limit order book," Papers 1511.04116, arXiv.org, revised Jun 2016.
    2. Iacopo Mastromatteo, 2014. "Apparent impact: the hidden cost of one-shot trades," Papers 1409.8497, arXiv.org, revised Jun 2015.
    3. Weibing Huang & Charles-Albert Lehalle & Mathieu Rosenbaum, 2015. "Simulating and Analyzing Order Book Data: The Queue-Reactive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 107-122, March.
    4. Marc Hoffmann & Mauricio Labadie & Charles-Albert Lehalle & Gilles Pagès & Huyên Pham & Mathieu Rosenbaum, 2013. "Optimization And Statistical Methods For High Frequency Finance," Post-Print hal-01102785, HAL.
    5. Aur'elien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Papers 1404.0648, arXiv.org, revised Jun 2015.
    6. Tzu-Wei Yang & Lingjiong Zhu, 2015. "A reduced-form model for level-1 limit order books," Papers 1508.07891, arXiv.org, revised Nov 2016.
    7. 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," Papers 1305.6323, arXiv.org, revised Aug 2015.
    8. Aurélien Alfonsi & Pierre Blanc, 2016. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Finance and Stochastics, Springer, vol. 20(1), pages 183-218, January.
    9. Emmanuel Bacry & Thibault Jaisson & Jean-Francois Muzy, 2014. "Estimation of slowly decreasing Hawkes kernels: Application to high frequency order book modelling," Papers 1412.7096, arXiv.org.
    10. Martin D. Gould & Julius Bonart, 2015. "Queue Imbalance as a One-Tick-Ahead Price Predictor in a Limit Order Book," Papers 1512.03492, arXiv.org.

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