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Continuous-time Modeling of Bid-Ask Spread and Price Dynamics in Limit Order Books

  • Jose Blanchet
  • Xinyun Chen
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    We derive a continuous time model for the joint evolution of the mid price and the bid-ask spread from a multiscale analysis of the whole limit order book (LOB) dynamics. We model the LOB as a multiclass queueing system and perform our asymptotic analysis using stylized features observed empirically. We argue that in the asymptotic regime supported by empirical observations the mid price and bid-ask-spread can be described using only certain parameters of the book (not the whole book itself). Our limit process is characterized by reflecting behavior and state-dependent jumps. Our analysis allows to explain certain characteristics observed in practice such as: the connection between power-law decaying tails in the volumes of the order book and the returns, as well as statistical properties of the long-run spread distribution.

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    File URL: http://arxiv.org/pdf/1310.1103
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    Paper provided by arXiv.org in its series Papers with number 1310.1103.

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    Date of creation: Oct 2013
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    Handle: RePEc:arx:papers:1310.1103
    Contact details of provider: Web page: http://arxiv.org/

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    1. Nikolaus Hautsch & Ruihong Huang, 2009. "The Market Impact of a Limit Order," SFB 649 Discussion Papers SFB649DP2009-051, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Ilija Zovko & J Doyne Farmer, 2002. "The power of patience: a behavioural regularity in limit-order placement," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 387-392.
    3. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    4. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    5. Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
    6. Matthieu Wyart & Jean-Philippe Bouchaud & Julien Kockelkoren & Marc Potters & Michele Vettorazzo, 2008. "Relation between bid-ask spread, impact and volatility in order-driven markets," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 41-57.
    7. Rama Cont & Adrien De Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
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