LOB-Impact Benchmark: Emergent Market Impact in Generative Limit Order Book Models

Injected metaorders elicit identifiable but too-steep impact laws in five neural LOB generators on five stocks, with no credible post-execution relaxation, while replay and kernel baselines behave as designed.

Generative LOB models are evaluated mainly by distributional similarity to historical streams, not by how they respond to an agent's own orders. When such simulators are used as world models, mispriced impact can teach policies that are optimal in simulation but wrong in the real market. Existing benchmarks measure counterfactual response only at the scale of a single event and do not separate mechanical impact from indirect reactions of other participants.

The benchmark injects execution-style metaorders into message-level generators and evaluates three phases: free generation, metaorder injection, and post-execution relaxation. Inputs are the model, stock, per-stock calibration, and n rollouts per direction per phase; injection schedule, calibration, and estimator are fixed before the model is run. Child size is the median market-order size, spacing follows eta=10% participation via Delta_N=9/phi, and daily volume normalizes cumulative participation; child count N=100 is fixed a priori. Each build-up injection is paired with a blind simulator-only control, and buy and sell experiments are combined by antisymmetrisation. The paper tests replay, parametric, and five neural generators on five NASDAQ stocks, with LOBSTER January 2026 calibration and book reconstruction via JAX-LOB.

• All five neural generators identify a law on every stock; all 25 intervals exclude 0.5, with exponents from 0.63 to 1.21. §3.4
• On AMD binned exponents are 0.66, 0.79, 0.87, 0.90, and 0.93, with 95% day-clustered bootstrap intervals of ± 0.05 – 0.06; no interval comes near 0.5. §3.2
• The neural panel shows Y=2.2–8.6 against empirical Y≈0.5; a 100-child metaorder moves simulated price by 17–70 bps versus at most 11 bps for any baseline. §3.2
• The visible peak is at least 3× the blind floor in all 25 neural cells and over 10× in 16, supporting C3. §3.2
• On AMD end-over-peak reads 1.19, 1.15, 1.16, 1.36, and 0.88, with post-execution slopes of +0.6, ±0.0, +0.4, +3.7, and -2.4% of peak per execution duration; no neural cell passes C5. §3.3
• The correlation between the LOB-Bench KS ranking and the impact ranking is unstable: +0.54 on GOOG and -0.71 on MSFT with p=0.02, and -0.90 within MSFT neural rows with p=0.08. §3.4

• The paper reports that impact decay during relaxation was not observed and tentatively attributes this to still-short context windows.
• The 4k-context variants fail the same tests but remain well short of a metaorder, so the attribution is untested rather than refuted.
• EA is outside the training corpus; the out-of-distribution result does not destroy the law but destroys its calibration.
• The blind arm behind C3 runs for the neural panel only, leaving attribution untested for baselines.

• Existing distributional benchmarks score spread, volume, inter-arrival, and imbalance distributions but are blind to counterfactual response to an agent's own orders. §1
• The benchmark takes four inputs and fixes injection schedule, calibration, and estimator before any model is run. §2.1
• In free generation the real AMD stream has gamma_flow=1.66 and H=0.54; no generator holds both legs, and every neural generator fails C1 with drift from +9 to -251 ticks. §3.1
• Historic replay shows no law; the neural panel passes C2 with sharp L2 misfit minima, while replay kernels are identified at delta=0.73–0.81 with Y=0.96–1.46. §3.2
• The blind control separates the model's reaction from book mechanics, and the visible-over-blind ratio attributes the excess impact to the model itself. §3.2
• Across 25 neural cells the same claim-ladder signature repeats: C1 fails, C2 and C3 pass, C4 and C5 fail. §3.4
• The authors suggest training toward empirical gamma_flow and H by learning replenishment rather than unlearning persistence, with longer contexts and larger models as the next test. §4