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Limit Order Books

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Limit Order Books

Martin D. Gould
Mason A. Porter
Stacy Williams
Mark McDonald
Daniel J. Fenn
Sam D. Howison
Published on 12/1/2010
Equities
Futures
Options
High frequency trading
Machine learning

This survey provides a comprehensive overview of limit order books (LOBs), which are used in over half of the world's financial markets. It defines key LOB concepts such as bid-ask spread, depth profiles, and order types, and discusses the challenges in studying LOBs, including state-space complexity, feedback loops, and hidden liquidity. The paper reviews empirical findings, highlighting stylized facts like the dependence of order arrival on relative prices and the non-trivial dynamics of price impact. It critically evaluates models from both economics (game-theoretic) and physics (stochastic) perspectives, noting that many models fail to reproduce key empirical features. The survey concludes by identifying unresolved problems, such as optimal execution strategies and the impact of different priority mechanisms, emphasizing the need for models that better capture real LOB behavior.

Highlights

  • 1Comprehensive survey of limit order book (LOB) empirical findings and models from both economics and physics perspectives.
  • 2Identifies key stylized facts of LOBs, including order flow, price impact, and spread dynamics.
  • 3Critically evaluates existing LOB models, highlighting discrepancies between model assumptions and empirical observations.
  • 4Outlines unresolved questions in LOB research, such as optimal execution and market stability.

Methods

  • M
    Statistical analysis of historical LOB data to uncover stylized facts.
  • M
    Zero-intelligence and perfect-rationality modeling approaches.
  • M
    Game-theoretic models from economics and stochastic models from physics.
  • M
    Monte Carlo simulation for complex LOB models.

Results

  • R
    Order arrival rates depend on relative prices rather than absolute prices.
  • R
    LOB state space is high-dimensional, requiring dimensionality reduction for modeling.
  • R
    Feedback between order flow and LOB state creates complex dynamics.
  • R
    Priority mechanisms (price-time, pro-rata, price-size) significantly influence trader behavior.
  • R
    Hidden liquidity (iceberg orders, dark pools) complicates empirical analysis.
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