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A Functional Limit Theorem for Limit Order Books with State Dependent Price Dynamics

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  • Christian Bayer
  • Ulrich Horst
  • Jinniao Qiu

Abstract

We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges in distribution to a fully coupled SDE-SPDE system when the order arrival rates tend to infinity and the impact of an individual order arrival on the book as well as the tick size tends to zero. The SDE describes the bid/ask price dynamics while the SPDE describes the volume dynamics.

Suggested Citation

  • Christian Bayer & Ulrich Horst & Jinniao Qiu, 2014. "A Functional Limit Theorem for Limit Order Books with State Dependent Price Dynamics," Papers 1405.5230, arXiv.org, revised Aug 2016.
  • Handle: RePEc:arx:papers:1405.5230
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    References listed on IDEAS

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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 & Dorte Kreher, 2016. "A diffusion approximation for limit order book models," Papers 1608.01795, arXiv.org, revised Aug 2017.
    3. Weibing Huang & Mathieu Rosenbaum, 2015. "Ergodicity and diffusivity of Markovian order book models: a general framework," Papers 1505.04936, arXiv.org.
    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.

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