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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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    Cited by:

    1. Ulrich Horst & Dorte Kreher, 2017. "Second order approximations for limit order books," Papers 1708.07394, arXiv.org, revised Mar 2018.
    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. Frank Kelly & Elena Yudovina, 2018. "A Markov Model of a Limit Order Book: Thresholds, Recurrence, and Trading Strategies," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 181-203, February.
    4. Ulrich Horst & Dörte Kreher, 2018. "Second order approximations for limit order books," Finance and Stochastics, Springer, vol. 22(4), pages 827-877, October.
    5. 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.
    6. Justin Sirignano, 2016. "Deep Learning for Limit Order Books," Papers 1601.01987, arXiv.org, revised Jul 2016.
    7. Horst, Ulrich & Kreher, Dörte, 2019. "A diffusion approximation for limit order book models," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4431-4479.
    8. 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.

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