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A diffusion approximation for limit order book models

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  • Horst, Ulrich
  • Kreher, Dörte

Abstract

This paper derives a diffusion approximation for a sequence of discrete-time one-sided limit order book models with non-linear state dependent order arrival and cancellation dynamics. The discrete time sequences are specified in terms of an R+-valued best bid price process and an Lloc2-valued volume process. It is shown that under suitable assumptions the sequence of interpolated discrete time models is relatively compact in a localized sense and that any limit point satisfies a certain infinite dimensional SDE. Under additional assumptions on the dependence structure we construct two classes of models, which fit in the general framework, such that the limiting SDE admits a unique solution and thus the discrete dynamics converge to a diffusion limit in a localized sense.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:11:p:4431-4479
    DOI: 10.1016/j.spa.2018.11.023
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    References listed on IDEAS

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    1. Xuefeng Gao & S. J. Deng, 2014. "Hydrodynamic limit of order book dynamics," Papers 1411.7502, arXiv.org, revised Feb 2016.
    2. Rama Cont & Adrien De Larrard, 2012. "Order book dynamics in liquid markets: limit theorems and diffusion approximations," Papers 1202.6412, arXiv.org.
    3. Cho, Nhansook, 1995. "Weak convergence of stochastic integrals driven by martingale measure," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 55-79, September.
    4. Xin Guo & Zhao Ruan & Lingjiong Zhu, 2015. "Dynamics of Order Positions and Related Queues in a Limit Order Book," Papers 1505.04810, arXiv.org, revised Oct 2015.
    5. Friedrich Hubalek & Paul Kruhner & Thorsten Rheinlander, 2017. "Brownian trading excursions and avalanches," Papers 1701.00993, arXiv.org.
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    Cited by:

    1. Cassandra Milbradt & Dorte Kreher, 2022. "A cross-border market model with limited transmission capacities," Papers 2207.01939, arXiv.org, revised Nov 2024.
    2. Ulrich Horst & Wei Xu, 2019. "The Microstructure of Stochastic Volatility Models with Self-Exciting Jump Dynamics," Papers 1911.12969, arXiv.org.

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