Bridging the Reality Gap in Limit Order Book Simulation

Abstract

We introduce a practical, interactive simulator of the limit order book for large-tick assets, designed to produce realistic execution, costs, and P&L. The book state is projected onto a tractable representation based on spread and volume imbalance, enabling robust estimation from market data. Event timing is calibrated to reproduce the fine-scale temporal structure of real markets, revealing a pronounced mode at exchange round-trip latency consistent with simultaneous reactions and latency races among participants. We further incorporate a feedback mechanism that accumulates signed trade flow through a power-law decay kernel, reproducing both concave market impact during execution and partial post-trade reversion. Across several stocks and strategy case studies, the simulator yields realistic behavior where profitability becomes highly sensitive to execution parameters. We present the approach as a practical recipe: project, estimate, validate, adapt, for building realistic limit order book simulations.

Figures (29)

• Figure 1: Order book with queues indexed relative to the current best bid and ask. The best queues $q_{-1}, q_1$ are never empty by definition. Deeper queues (dashed) may be empty.
• Figure 2: Price move after the best ask $q_1$ is fully depleted by a trade. Since $q_2$ was empty, the old $q_3$ becomes the new $q_1$: the best ask jumps from $30.02 to $30.04 and the mid-price moves from $30.01 to $30.02, a one-tick upward move. The newly revealed deeper queues (green) are sampled from the empirical stationary distribution.
• Figure 3: A limit order placed inside the spread narrows it. A bid limit order at $30.01 creates a new best bid, shifting all bid queues: the spread narrows from $n=2$ to $n=1$.
• Figure 4: Imbalance binning scheme. Bins have width $0.1$; the $0$ bin (highlighted) captures exact balance only. Three example values and their bin assignments are shown.
• Figure 5: Left: Observation count per imbalance bin; the $0$ bin is more populated than highly imbalanced books. Centre: Average inter-event time $\mathbb{E}[\Delta t \mid \text{Imb}, n=1]$ per imbalance bin; extreme imbalances correspond to faster activity. Right: Event probabilities at the best bid $q_{-1}$ given imbalance ($n=1$). Positive imbalance means $q_{-1} > q_1$; probabilities do not sum to 1 since other queues also receive events. All statistics were calibrated on data spanning $12/2023 \rightarrow 12/2025$.