Bridging the Reality Gap in Limit Order Book Simulation¶

Authors: Patrick Noble (Jump Trading), Mathieu Rosenbaum (Université Paris Dauphine-PSL), Saad Souilmi (École Polytechnique) Year: 2026 (March 2026) arXiv: 2603.24137 Categories: q-fin.TR

Plain-language abstract¶

Electronic market participants (market makers, prop firms, brokerages) rely on LOB simulators to stress-test strategies before going live. Existing zero-intelligence and queue-reactive models fit first-order statistics but fail on two dimensions that matter for strategy evaluation: (i) inter-event times are not exponential — real markets exhibit pronounced clustering at exchange round-trip latency from latency races, and (ii) a metaorder leaves no market impact after completion, so simulated P&L systematically overstates profit and understates risk. This paper extends the Huang–Rosenbaum Queue-Reactive (QR) model with three modifications that turn it into a practical, interactive simulator for large-tick assets.

Key contributions¶

State projection onto $(\text{Imb}, n)$ — collapse the high-dimensional queue state into a 2D representation of volume imbalance at the best level + spread in ticks. Keeps the bid-ask cross-dependence in a single scalar and makes empirical estimation tractable (the full queue-by-queue conditioning is too sparse).
Non-exponential inter-event times — replace the Markov Poisson assumption with a flexible empirical distribution. This reveals a sharp mode at the exchange round-trip latency consistent with simultaneous reactions and latency races (Aquilina et al. 2021: ~20% of volume).
Power-law market-impact feedback kernel — accumulate signed trade flow, bias subsequent trades toward mean reversion. Reproduces two well-known empirical facts: concave impact during execution (square-root law) and partial reversion after (impact decay). The same mechanism can inject custom signals into book dynamics.
Random order volumes — replace unit sizes (vanilla QR) with state-conditional empirical size distributions, capped at 50 × median event size. Queue depletion then emerges naturally whenever a small best queue is hit by a moderate trade, eliminating the need for a special "depletion" event type.
Methodology framed as a recipe — project → estimate → validate → adapt — rather than a rigid model. Practitioners decide which features matter for their asset and strategy.

Method summary¶

Data¶

4 S&P 500 large-tick stocks around $30: INTC, VZ, T, PFE.
Databento L2 data, December 2023 → December 2025 (~2 years).
Paper illustrates results on PFE; equivalents for the other three in the appendix.
Code available on GitHub.

State projection¶

\[\Phi(\text{LOB}) = (\text{Imb}, n), \qquad \text{Imb} = \frac{q_{-1} - q_1}{q_{-1} + q_1}\]

$\text{Imb}$ discretised into 21 bins of width 0.1; special point bin at $\text{Imb}=0$ to avoid mixing opposite signs.
$n$ = spread in ticks (for large-tick assets, typically $n = 1$; $n \geq 2$ is transient and resolved by CreateBid/CreateAsk events).
Queue sizes normalised by median event size (MES) per level, more robust than the mean used in original QR.
Optional extra dim $\ell = q_{-1} + q_1$ (total resting size) was tested but did not significantly improve the reproducing power while diluting observations — rejected.

Event space¶

$e = (\mathcal{T}, s, i)$ with type $\mathcal{T} \in \{\text{Add, Cancel, Trade, CreateBid, CreateAsk}\}$, side $s \in \{-1, +1\}$, queue level $i$.

Adds/Cancels target queues up to $q_{\pm 2}$.
Trades target only the best queues $q_{\pm 1}$ (marketable limit orders); "walk-the-book" trades are aggregated into a single total-volume trade.
Create events: a new best on either side when the spread opens; the subsequent burst of Adds at the new price is aggregated into the Create's size.

Market-impact feedback¶

A power-law decay kernel accumulates signed trade flow and biases subsequent trade intensities:

\[I_t = \sum_{s < t} \text{sign}(v_s) \cdot |v_s|^\alpha \cdot \phi(t - s), \qquad \phi(\tau) \propto \tau^{-\beta}\]

This reproduces (a) concave impact during execution and (b) partial reversion after — both essential for realistic strategy evaluation. The same mechanism can be repurposed to inject exogenous alpha signals.

Validation¶

Simulated vs empirical statistics compared on: imbalance-conditional event probabilities, inter-event time distributions (showing the round-trip-latency mode), spread dynamics, and impact response curves. PFE traces reproduce the fine-scale temporal structure; the QR-exponential baseline flattens it.

Case studies¶

Mid-frequency signal-based strategy — reveals how profitability depends on execution parameters when the simulator correctly models market impact.
High-frequency imbalance strategy — demonstrates that naïve QR without the latency-race mode and impact feedback overstates realised P&L by an economically meaningful margin.

Limitations¶

Large-tick assets only: the state projection relies on $n = 1$ being the dominant regime (<5% of trades on PFE happen at $n \geq 2$). Small-tick equities (GOOG, CHTR etc. in deep-lob-forecasting) would require a different representation.
Four-stock sample: all INTC / VZ / T / PFE near $30 — no generalisation test across price levels or sectors.
Point-in-time kernel calibration: the impact kernel is fit on one window; regime changes (e.g., around earnings or macro events) are not modelled.
Walk-the-book events aggregated, not explicitly modelled: acceptable given their rarity, but a simulator targeting crash periods would need to treat them separately.

Connections¶

The QR framework this paper builds on is worth a dedicated method page: queue-reactive-model.
Volume imbalance is the central state variable, linking directly to order-flow-imbalance and to microprice (Stoikov 2018) as a continuous latent price within the spread — the same mechanism explainable-crypto-microstructure validates in crypto via the W/USDT spot-vs-perp experiment ($c = 0.94$).
The large-tick focus reinforces the cross-paper tick-size finding surfaced by re-ingest: large-tick assets are where queue-imbalance signals are readable and simulatable; small-tick assets require different machinery (see deep-learning-meets-market-microstructure).
Power-law impact kernel matches the Bacry et al. (2016) Hawkes-based impact literature referenced by forecasting-high-frequency-ofi and order-flow-filtration.
Practical implication for backtesting: the taker/maker divergence in explainable-crypto-microstructure's flash crash would likely be much sharper in a simulator with this paper's impact feedback than in a naïve QR baseline.