Bridging the Reality Gap in Limit Order Book Simulation

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Bridging the Reality Gap in Limit Order Book Simulation

Patrick Noble
Mathieu Rosenbaum
Saad Souilmi
Published on 3/25/2026
Equities
Stocks
High frequency trading
Machine learning
Market timing
Risk management

This paper introduces a practical, interactive simulator of the limit order book for large-tick assets, designed to produce realistic execution costs and P&L for strategy evaluation. The authors extend the queue-reactive (QR) model with three key modifications: a state projection onto spread and volume imbalance for robust estimation, a non-exponential inter-event time distribution that captures the clustering of events at exchange round-trip latency (revealing latency races among participants), and a market impact feedback mechanism that accumulates signed trade flow through a power-law decay kernel, reproducing concave impact during execution and partial post-trade reversion. The simulator is validated on four S&P 500 stocks using two years of data, showing that it reproduces marginal statistics such as event-type frequencies, imbalance before trades, and volatility, while addressing the limitations of the original QR model in inter-event time distribution and market impact. Two case studies—a mid-frequency signal-based strategy and a high-frequency imbalance strategy—demonstrate that the simulator yields realistic behavior where profitability becomes highly sensitive to execution parameters, making it a valuable tool for practitioners. The approach is presented as a practical recipe: project the book onto a tractable state, estimate conditional distributions from data, validate against empirical statistics, and adapt to the asset or use case.

Highlights

  • 1Introduces a practical, interactive limit order book simulator for large-tick assets that projects the book state onto spread and volume imbalance, enabling robust estimation from market data.
  • 2Replaces the exponential inter-event time assumption of queue-reactive models with a flexible distribution that captures a pronounced mode at exchange round-trip latency, modeling competitive fill dynamics and latency races.
  • 3Incorporates a market impact feedback mechanism using a power-law decay kernel on signed trade flow, reproducing concave impact during execution and partial post-trade reversion.
  • 4Validates the simulator across multiple stocks and strategy case studies, demonstrating realistic behavior where profitability is highly sensitive to execution parameters.
  • 5Presents a practical recipe: project, estimate, validate, adapt, for building realistic limit order book simulations.

Methods

  • M
    Queue-reactive (QR) model with state projection onto volume imbalance and spread, discretized into bins for tractable estimation.
  • M
    Non-exponential inter-event time distribution calibrated via Gaussian mixture model to capture latency races and exchange round-trip latency.
  • M
    Market impact feedback mechanism: accumulated signed trade flow with power-law decay kernel biases subsequent trade probabilities toward mean reversion.
  • M
    Maximum likelihood estimation of event probabilities, total intensities, and volume distributions from empirical data, with symmetrization between bid and ask.

Results

  • R
    The baseline QR model reproduces event-type distributions, imbalance before trades, hourly traded volume, and five-minute realized volatility accurately, but underestimates tail returns.
  • R
    Inter-event times exhibit a pronounced mode at ~29 microseconds, corresponding to exchange round-trip latency, with ~25% of events occurring faster than this mode, indicating latency races.
  • R
    The market impact feedback mechanism produces concave price impact during metaorder execution and partial reversion after, matching empirical observations, unlike the baseline model.
  • R
    In strategy case studies, the simulator reveals that profitability is highly sensitive to execution parameters, with realistic trade-offs between fill rates and adverse selection.
  • R
    The model adapts well across multiple large-tick stocks (INTC, VZ, T, PFE), with parameter stability over time.
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