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

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  • He Huang
  • Alec N. Kercheval

Abstract

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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    Citations

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    Cited by:

    1. Korolev, V.Yu. & Chertok, A.V. & Korchagin, A.Yu. & Zeifman, A.I., 2015. "Modeling high-frequency order flow imbalance by functional limit theorems for two-sided risk processes," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 224-241.
    2. M. Shabani & M. Magris & George Tzagkarakis & J. Kanniainen & A. Iosifidis, 2023. "Predicting the state of synchronization of financial time series using cross recurrence plots," Post-Print hal-04415269, HAL.
    3. Efstathios Panayi & Gareth W. Peters, 2015. "Stochastic simulation framework for the limit order book using liquidity-motivated agents," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-52.
    4. Mostafa Shabani & Martin Magris & George Tzagkarakis & Juho Kanniainen & Alexandros Iosifidis, 2022. "Predicting the State of Synchronization of Financial Time Series using Cross Recurrence Plots," Papers 2210.14605, arXiv.org, revised Nov 2022.
    5. Tzu-Wei Yang & Lingjiong Zhu, 2015. "A reduced-form model for level-1 limit order books," Papers 1508.07891, arXiv.org, revised Nov 2016.
    6. Sim, Min Kyu & Deng, Shijie, 2020. "Estimation of level-I hidden liquidity using the dynamics of limit order-book," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    7. Efstathios Panayi & Gareth Peters, 2015. "Stochastic simulation framework for the Limit Order Book using liquidity motivated agents," Papers 1501.02447, arXiv.org, revised Jan 2015.
    8. Hanchao Liu, 2020. "When one stock share is a biological individual: a stylized simulation of the population dynamics in an order-driven market," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 373-408, June.
    9. Mynbaev, Kairat, 2020. "Using full limit order book for price jump prediction," MPRA Paper 101684, University Library of Munich, Germany.

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