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Hydrodynamic limit of order book dynamics

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  • Xuefeng Gao
  • S. J. Deng

Abstract

In this paper, we establish a fluid limit for a two--sided Markov order book model. Our main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the "sell-side shape" and "buy-side shape" of an order book converges to a pair of deterministic measure-valued processes in a certain sense. We also test our fluid approximation on data. The empirical results suggest that the approximation is reasonably good for liquidly--traded stocks in certain time periods.

Suggested Citation

  • Xuefeng Gao & S. J. Deng, 2014. "Hydrodynamic limit of order book dynamics," Papers 1411.7502, arXiv.org, revised Feb 2016.
  • Handle: RePEc:arx:papers:1411.7502
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    References listed on IDEAS

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    16. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
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    Cited by:

    1. Frank Kelly & Elena Yudovina, 2015. "A Markov model of a limit order book: thresholds, recurrence, and trading strategies," Papers 1504.00579, arXiv.org, revised Mar 2017.
    2. Ulrich Horst & Wei Xu, 2017. "A Scaling Limit for Limit Order Books Driven by Hawkes Processes," Papers 1709.01292, arXiv.org, revised Aug 2018.
    3. repec:spr:finsto:v:22:y:2018:i:4:d:10.1007_s00780-018-0373-7 is not listed on IDEAS
    4. Ulrich Horst & Dorte Kreher, 2015. "A weak law of large numbers for a limit order book model with fully state dependent order dynamics," Papers 1502.04359, arXiv.org, revised May 2016.
    5. Justin Sirignano, 2016. "Deep Learning for Limit Order Books," Papers 1601.01987, arXiv.org, revised Jul 2016.

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