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A generalized birth--death stochastic model for high-frequency order book dynamics


  • He Huang
  • Alec N. Kercheval


We use a generalized birth--death stochastic process to model the high-frequency dynamics of the limit order book, and illustrate it using parameters estimated from Level II data for a stock on the London Stock Exchange. A new feature of this model is that limit orders are allowed to arrive in multiple sizes, an important empirical feature of the order book. We can compute various quantities of interest without resorting to simulation, conditional on the state of the order book, such as the probability that the next move of the mid-price will be upward, or the probability, as a function of order size, that a limit ask order will be executed before a downward move in the mid-price. This generalizes the successful model of Cont et al. [ Oper. Res. , 2010, 58 , 549--563] by means of a new technical approach to computing the distribution of first passage times.

Suggested Citation

  • He Huang & Alec N. Kercheval, 2012. "A generalized birth--death stochastic model for high-frequency order book dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 12(4), pages 547-557, August.
  • Handle: RePEc:taf:quantf:v:12:y:2012:i:4:p:547-557
    DOI: 10.1080/14697688.2012.664926

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    Cited by:

    1. repec:eee:apmaco:v:253:y:2015:i:c:p:224-241 is not listed on IDEAS
    2. Efstathios Panayi & Gareth Peters, 2015. "Stochastic simulation framework for the Limit Order Book using liquidity motivated agents," Papers 1501.02447,, revised Jan 2015.
    3. Tzu-Wei Yang & Lingjiong Zhu, 2015. "A reduced-form model for level-1 limit order books," Papers 1508.07891,, revised Nov 2016.

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