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Price Dynamics in a Markovian Limit Order Market

Author

Listed:
  • Rama Cont

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

  • Adrien de Larrard

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical tractability, the model allows to obtain analytical expressions for various quantities of interest such as the distribution of the duration between price changes, the distribution and autocorrelation of price changes, and the probability of an upward move in the price, conditional on the state of the order book. We study the diffusion limit of the price process and express the volatility of price changes in terms of parameters describing the arrival rates of buy and sell orders and cancelations. These analytical results provide some insight into the relation between order flow and price dynamics in order-driven markets.

Suggested Citation

  • Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    • Handle: RePEc:hal:journl:hal-00552252
    DOI: 10.1137/110856605
    Note: View the original document on HAL open archive server: https://hal.science/hal-00552252v4
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    References listed on IDEAS

    as
    1. Burton Hollifield & Robert A. Miller & Patrik Sandås, 2004. "Empirical Analysis of Limit Order Markets," Review of Economic Studies, Oxford University Press, vol. 71(4), pages 1027-1063.
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    Full references (including those not matched with items on IDEAS)

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    Keywords

    limit order book; market microstructure; queueing; diffusion limit; high-frequency data; liquidity; duration analysis; point process;
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