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From Glosten-Milgrom to the whole limit order book and applications to financial regulation

Author

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  • Weibing Huang
  • Mathieu Rosenbaum
  • Pamela Saliba

Abstract

We build an agent-based model for the order book with three types of market participants: informed trader, noise trader and competitive market makers. Using a Glosten-Milgrom like approach, we are able to deduce the whole limit order book (bid-ask spread and volume available at each price) from the interactions between the different agents. More precisely, we obtain a link between efficient price dynamic, proportion of trades due to the noise trader, traded volume, bid-ask spread and equilibrium limit order book state. With this model, we provide a relevant tool for regulators and market platforms. We show for example that it allows us to forecast consequences of a tick size change on the microstructure of an asset. It also enables us to value quantitatively the queue position of a limit order in the book.

Suggested Citation

  • Weibing Huang & Mathieu Rosenbaum & Pamela Saliba, 2019. "From Glosten-Milgrom to the whole limit order book and applications to financial regulation," Papers 1902.10743, arXiv.org.
    • Handle: RePEc:arx:papers:1902.10743
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    References listed on IDEAS

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    Cited by:

    1. Bastien Baldacci & Dylan Possamai & Mathieu Rosenbaum, 2019. "Optimal make take fees in a multi market maker environment," Papers 1907.11053, arXiv.org, revised Mar 2021.
    2. Bastien Baldacci & Philippe Bergault & Joffrey Derchu & Mathieu Rosenbaum, 2020. "On bid and ask side-specific tick sizes," Papers 2005.14126, arXiv.org, revised May 2020.
    3. Mouhamad Drame, 2020. "Limit Order Book (LOB) shape modeling in presence of heterogeneously informed market participants," Papers 2009.02808, arXiv.org.
    4. Joffrey Derchu & Dimitrios Kavvathas & Thibaut Mastrolia & Mathieu Rosenbaum, 2023. "Equilibria and incentives for illiquid auction markets," Papers 2307.15805, arXiv.org.

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