mbo-queue

Exact FIFO queue reconstruction from CME market-by-order (MBO) data, and a benchmark of the queue-position estimators that market-making backtests use when they only see aggregate depth.

Why

A backtest of a passive (resting) order has to guess where that order sits in the queue, because most market data (market-by-price, MBP) only shows the total size at each price. When the size at your price drops and no trade printed, someone cancelled, but were they ahead of you or behind you? Open-source backtesters answer with a family of rules: hftbacktest's RiskAdverseQueueModel (cancels are always behind you) and its probabilistic power and log models, which follow Rigtorp's estimator.

CME MBO data, as distributed by Databento, carries an order ID on every add, cancel, modify and fill, so the true queue can be rebuilt. mbo-queue rebuilds it and measures how wrong each estimator is: in queue position, in fill rate, in fill time, and in the P&L of a passive order.

What it computes

Each item is one section of SPEC.md, which is the rule set both engines implement.

1. Input. A single-instrument stream of Databento MBO records, read in file order and only at event boundaries (records ending with the F_LAST flag).
2. Book rebuild. Adds join the back of their price level, size increases and price changes lose priority, size decreases keep it, fills leave the book through the cancel or modify that follows them, and a native iceberg refill goes to the back as it does at CME.
3. FIFO-consistency rate. For every fill, whether the filled order is the one the rebuild says is at the front; this is the quality gate (at least 95%) before trusting queue positions.
4. Shadow orders. A hypothetical order placed at the back of the best level, whose true queue position is the remaining size of the specific orders that were ahead of it (no market impact).
5. MBP estimators. Six queue-position rules (risk_averse, prob_power1/2/3, prob_log, front_optimistic) run on the same shadows while seeing only aggregate depth and trade prints.
6. Resting-order labels. For every real order near the touch: queue ahead at entry, distance from the best price, and its outcome (filled, cancelled, moved, requeued, cleared, censored) with the time to that outcome, for competing-risks fill models.
7. Book samples. The top N levels at requested times, for reconciliation with MBP-10 and for mid-price paths.
8. Queue-position snapshots. At requested times, every real resting order at the best levels with its rank, size and size ahead, read without look-ahead.
9. Order-anchored tracks. The six estimators run for real orders instead of hypothetical ones and scored against each order's own fill records, optionally keeping them running after the true fill (a horizon H) so that late estimated fills are measured.

scripts/run_day.py turns these outputs into per-estimator metrics: fill-rate bias, false and missed fills, queue-position error, fill-time error, markouts at +1 s and +10 s, and a split of the P&L bias into a fill-count part and an adverse-selection-given-a-fill part: P&L_est - P&L_true = (N_est - N_true) * m_true + N_est * (m_est - m_true).

Install

pip install mbo-queue            # the engines; needs only numpy
pip install "mbo-queue[data]"    # plus databento, pandas and pyarrow, to read DBN files

Wheels are built for CPython 3.10 to 3.14 on Linux (x86_64, aarch64) and macOS (arm64, x86_64). Elsewhere pip builds from source, which needs a C++20 compiler.

Quickstart

Run the six estimators against the true queue on the built-in synthetic exchange, where cancels hit resting orders in proportion to their size:

import numpy as np
from mboq import fast
from mboq.reference import ESTIMATORS
from mboq.synthetic import generate

rec, _, _, ex = generate(n_events=30_000, seed=1, cancel_mode="volume", p_modify=0.0)
ts = rec["ts_event"].astype(np.int64)
place = np.arange(ts[200], ts[-1] - 120_000_000, 100_000_000)       # a shadow every 100 ms
sh = fast.run(rec, tick=ex.tick, place_times=place, horizon_ns=60_000_000)["shadows"]
ok = sh["end"] != 2                                                  # drop shadows cut by a clear
nobs, true_fill = sh["nobs"][ok].sum(), sh["true_filled"][ok].mean()
print(f"{'estimator':<18}{'queue error (lots)':>20}{'fill-rate bias (pp)':>22}")
for k, name in enumerate(ESTIMATORS):
    err = sh["err_sum"][ok, k].sum() / nobs
    bias = 100 * (sh["est_filled"][ok, k].mean() - true_fill)
    print(f"{name:<18}{err:>+20.3f}{bias:>+22.2f}")

Output (synthetic data):

estimator           queue error (lots)   fill-rate bias (pp)
risk_averse                     +1.738                 -1.00
prob_power1                     -0.028                 -0.42
prob_power2                     -0.109                 -0.50
prob_power3                     -0.119                 -0.42
prob_log                        +0.548                 -0.25
front_optimistic                -0.246                 +0.50

risk_averse assumes every cancel is behind you, so it thinks the queue ahead is longer than it is; the linear model (prob_power1) is close to unbiased here because that is how this synthetic exchange chooses which order cancels.

mboq.fast.run (C++) and mboq.reference.Reference(...).run (pure Python) take the same records and return the same dict of numpy arrays: stats, fifo_rank, shadows, labels, samples, queue, and tracks with order_tracks=True.

Running on Databento data

python scripts/run_day.py --mbo session.mbo.dbn.zst --mbp10 session.mbp-10.dbn.zst \
    --tick 0.01 --day YYYY-MM-DD --label CLZ6 --release-et 10:30
python scripts/run_day.py --synthetic          # the same pipeline on synthetic data

The MBO file must cover the whole session, because the book can only be rebuilt from Databento's 00:00 UTC snapshot. run_day.py places a bid and an ask shadow every second, scores the six estimators overall and in a window around a scheduled release time, reconciles the rebuilt book with MBP-10 if given, and writes summary.json (with input SHA-256s and the run configuration) and report.md. Results computed from licensed market data are covered by that data's license.

How it is validated

Everything below runs in the test suite or the scripts in this repository, on synthetic data.

• Known answers per estimator and regime. The synthetic CME-style FIFO exchange (mboq/synthetic.py) emits Databento-format records and has a switch for where in the queue cancels happen, so the right answer is known. scripts/synthetic_validation.py (5 seeds, 30,000 events each):

  cancel regime	expected	result
  at the tail	risk_averse exact	zero queue error, zero fill-rate bias
  at the front	front_optimistic exact	zero queue error, zero fill-rate bias
  proportional to size	linear model close to unbiased	mean queue error -0.022 lots (s.d. 0.040 across seeds) vs +1.769 for risk_averse
  proportional to order count	linear model close to unbiased	mean queue error +0.003 lots (s.d. 0.030) vs +1.710 for risk_averse

• Rebuild equals the exchange. The rebuilt book and queues equal the generator's own at every sampled event in all four regimes, including book clears, snapshots without a clear, native iceberg refills and fills listed out of priority order; FIFO-consistency is then exactly 100%.

• Two independent implementations, bitwise equal. The Python reference (explicit ahead sets) and the C++20 core (priority stamps and intrusive lists) return byte-identical output (every counter and array: dtype, shape and bytes) on randomized streams with every feature switched on. The C++ core is compiled with -ffp-contract=off so no fused multiply-add breaks this.

• Hand-computed scenarios for each rule: cancel ahead vs behind, priority loss, trade-through, FIFO violations, label outcomes, iceberg refills, out-of-order fills, every track and horizon case.

• No look-ahead. Book samples and queue snapshots before time T do not change when every record after T is scrambled or deleted.

• Backward compatibility. Each new feature is off by default, and turning it off reproduces the earlier version. Stored SHA-256 digests of earlier versions' outputs are checked in full on macOS arm64, where they were recorded. The estimators' floating-point state goes through the system math library (pow, log1p), whose last bits can differ between platforms. So elsewhere only the input streams and the book outputs (labels, FIFO ranks, samples, queue rows) are compared with stored digests, and the flag-off/flag-on equalities are checked within the run.

• Real decode path. One test decodes Databento's public 4-record sample file (fetched by scripts/fetch_test_data.sh, pinned by commit and SHA-256; the test skips without it).

bash scripts/fetch_test_data.sh      # optional: the DBN decode test
python tests/test_mboq.py            # 51 tests (or: pytest tests)
python scripts/synthetic_validation.py

Performance

Synthetic stream from scripts/bench.py (229,313 records, 5,838 shadow placements, 28,588 order tracks), one thread, Apple M3, macOS, Python 3.10, mbo-queue 0.6.0 built from the sdist. Every run checks that the C++ and Python outputs are identical.

Order tracks are off by default and cost nothing when off. When they are on, most of the time goes to the per-track estimator updates the spec requires at every touched level. pow and log1p stay library calls so that the C++ output matches Python bit for bit.

Limitations

• Displayed outright book only. MBO does not include implied (spread-generated) liquidity or the hidden part of iceberg orders, so "truth" here is the order-ID-resolved displayed outright book. Its quality is measured (FIFO-consistency, MBP-10 reconciliation), not assumed.
• No-impact shadows. A shadow order never trades and does not change anyone's behaviour, the same assumption every replay backtester makes; results apply to small orders. Order-anchored tracks (section 9) use real orders, at the price of selection (orders that joined at the touch are not a random sample of placements).
• Snapshot ordering. Snapshot records are assumed to arrive in queue order within each price level (SPEC assumption A1). The FIFO-consistency gate tests this on every file.
• CME semantics. The rebuild rules are those of Databento's CME Globex MBO feed. Other venues may need different rules.

Research use

mbo-queue underpins an order-level study of liquidity in CME energy futures (paper forthcoming). This repository contains only the engine, its synthetic tests and generic scripts; no market data and no results computed from market data.

How to cite

See CITATION.cff, or:

Dani, A. (2026). mbo-queue: exact FIFO queue reconstruction from CME market-by-order data and a benchmark of MBP queue-position estimators (version 0.6.0). https://github.com/AnshDani2004/mbo-queue

Layout

SPEC.md (the rules) · src/mboq/reference.py (readable Python) · cpp/mboq_core.cpp (C++20 + pybind11) · src/mboq/fast.py (the C++ wrapper) · src/mboq/synthetic.py (known-answer exchange) · src/mboq/io.py (DBN loading) · scripts/ · tests/ · CHANGELOG.md.

License

MIT for the code (see LICENSE). No market data is included in this repository or its packages.