Avellaneda–Stoikov Market Maker on Crypto Perpetual Futures

A research-grade C++20 walk-forward backtester for the Avellaneda–Stoikov (AS) inventory-aware market-making policy, applied to Coincall BTCUSD perpetual futures. It calibrates the model's parameters (volatility, fill intensity) on rolling historical windows and replays out-of-sample quoting against the real trade tape — no synthetic fills, no in-sample leakage.

The goal is honest: establish whether the textbook AS policy delivers a positive risk-adjusted edge on a high-volatility, fee-light venue, and to expose the failure modes that prevent it from doing so in practice.

Status. Engine stable; test suite green (24 / 24). Best configuration over 185 walk-forward windows (24 h calibration / 1 h OOS, Jun 14–23 2026, Coincall BTCUSD perp): Total PnL +$38.04 · Mean Sharpe 1.84 · 69.7 % profitable windows · 46,799 fills. See Results and docs/design_findings.md for the full journey from −$74 (v2) to +$38 (v4) and the design decisions that drove it.

---

Pipeline

load ──► calibrate ──► simulate ──► write
 │           │             │           │
 │           │             │           └─ per-window CSVs + aggregate summary
 │           │             └───────────── quote-through fill replay vs. real tape
 │           └─────────────────────────── Roll σ + intensity (A, κ) by MLE
 └─────────────────────────────────────── Parquet OB snapshots + trade tape (DuckDB glob)

The model posts quotes around an inventory-adjusted reservation price rather than the mid:

reservation price   r  = s − q·(γσ² + f)·τ
optimal half-spread δ* = ½·γσ²τ + (1/γ)·ln(1 + γ/κ)
posted quotes          bid = r − δ*,   ask = r + δ*

where s = mid, q = signed inventory (lots), γ = risk aversion, σ = per-snapshot volatility, κ, A = exponential fill-intensity parameters (Λ(δ) = A·e^{−κδ}), f = funding rate (currently 0), and τ = a stationary risk horizon (see below).

---

Key architectural choices

1. Walk-forward, not a single backtest. Parameters (σ, κ, A) are calibrated on a rolling calibration slice and the policy is executed on the next, disjoint slice. Calibration indices are always strictly before out-of-sample indices — an invariant enforced by the test_walk_forward_no_lookahead unit test. This is the firewall against the look-ahead bias that quietly inflates most naïve MM backtests.

2. Quote-through fill replay, not Poisson simulation. A bid fills only when a real tape trade crosses below our live bid (trade.price < bid); symmetric for the ask. No synthetic intensity draws. This grounds PnL in the actual tape instead of in the model's own fill assumption — the intensity parameters (A, κ) feed only the spread, never the fills themselves.

3. Stationary horizon for a no-expiry instrument. Perpetuals have no terminal, so the classic τ = T − t is undefined. We replace it with a fixed risk-budget horizon τ_risk, recovering the infinite-horizon stationary AS of Guéant–Lehalle–Fernández-Tapia. τ_risk is volatility-scaled per window:

τ_risk(σ) = B / (γ · σ^α)      ⇒      risk term  ½γσ²τ = B·σ^(2−α)/2

α = 1 (the default) makes the half-spread scale linearly in σ rather than quadratically — adverse selection per fill (≈ σ·√τ) becomes roughly constant across volatility regimes. This single change cut extreme-vol losses by ~87%.

4. Realistic recalibration handoff. When a window rolls, the fill engine keeps quoting on stale parameters until the measured calibration latency elapses, then atomically switches to the live parameters — modelling the real cost of a recal cycle rather than assuming an instantaneous swap.

5. Defensive execution details.

• Order latency — a quote computed at tick t is not fillable until t + 50 ms.
• Glitch filter — on an anomalous mid jump (|Δmid| > 5σ) the engine cancels both the live and the pending quote slot, so stale prices can't be hit.
• Hard inventory bounds — enforced both as a quote-side suppression and as a fill-time backstop, complementing (not replacing) the AS skew.

6. Notional-anchored sizing. Quotes are sized in integer lots (default 0.001 BTC ≈ $65). --lot-notional back-solves the lot from a target USD notional so results are comparable across price levels.

---

Build & run

Dependencies via Homebrew:

brew install nlopt duckdb fmt

Configure and build (Release with -O3):

cmake -S . -B build -DCMAKE_BUILD_TYPE=Release
cmake --build build -j$(nproc)

Run the backtester (the CLI defaults already encode the best configuration):

./build/wf_backtest \
  --ob-glob     "/path/to/btcusd_2*.parquet" \
  --trades-glob "/path/to/btcusd_trades_*.parquet" \
  --out         results

Run the tests:

./build/run_tests        # or: cd build && ctest --output-on-failure

Selected CLI flags

Flag	Meaning	Default
--cal-hours	Calibration window length (h)	24
--recal-hours	Out-of-sample / recal cadence (h)	1
--gamma	AS risk-aversion γ	0.1
--vol-budget	B in τ = B/(γ·σ^α); sets half-spread ≈ B·σ/2	0.5
--sigma-min	Suppress quoting when calibrated σ < threshold	0
--min-spread-bps	Absolute minimum half-spread floor (bps of mid)	0
--cancel-drift	Cancel stale side when mid drifts > N·σ from quote	0
--vol-exponent	α in the adaptive-τ formula	1.0
--q-max / --q-min	Hard inventory bounds (lots)	±5
--lot-size	Lot size in BTC	0.001
--lot-notional	If > 0, lot_size = USD / first_mid	0
--glitch-sigma	Mid-jump cancel-all threshold (σ units)	5.0
--order-latency-ms	Synthetic order-ack latency (ms)	50

A full reference lives in docs/as_perpetual_handoff.md.

Output

Written to --out/: window_results.csv, fills_log.csv, quotes_log.csv, pnl_series.csv, and a summary.txt roll-up.

---

Results

All runs: γ = 0.1, lot = 0.001 BTC, 50 ms order latency, 5σ glitch filter, Coincall BTCUSD perpetual OB + trades.

Version evolution — Jun 14–22 2026 (full dataset, 174 windows)

Version	Key change	PnL	Fills	Mean RS/fill	% Profitable
Baseline	Original binary	−$256.94	480	–	–
v2	Recal-latency fix	−$73.95	936	−$68.05	6.7 %
v3	Hybrid τ + fractional inventory	−$17.23	95	+$37.24	47.1 %
v4 (default)	vol_budget = 0.5 (tight quoting)	+$38.04	46,799	+$2.92	69.7 %

v4 headline metrics (Jun 14–23 2026 · 185 windows · 1 h OOS)

Metric	Value
Total PnL	+$38.04
Mean Sharpe	1.84 ± 2.78
% Profitable windows	69.7 %
Total fills	46,799 (7 % fill rate of tape trades)
Mean realized spread	+$2.92 / fill
Negative-spread fills	13.1 %
Max single-window drawdown	$15.53
Valid fills (correct trade direction)	51.2 %
Stale fills (quote drifted past touch)	48.8 % ($2–4 inversion, price-improved in real LOB)

What drove the improvements

v2 → v3 (hybrid τ): The AS formula with high inventory and vol_budget=5 produced asks far below mid (ask ≈ mid − $462 at q=5, σ=20). Every buy trade triggered a fill, generating 3 k+ fills with mean RS −$68. The hybrid τ fix uses a separate τ_inv for the inventory skew, set so ask = mid exactly at q_max regardless of σ. Zero inverted quotes after this change.

v3 → v4 (vol_budget 5→0.5): With hybrid τ curing inversions, the remaining problem was too-wide spreads (half-spread ≈ $54 at the old default vs. OB half-spread $5.40). Only 0.5 % of trades moved far enough from mid to trigger a fill. Reducing vol_budget to 0.5 tightens the half-spread to ≈$3–9, at the OB touch. Fill count jumped from 95 to 43 k and the strategy turned profitable by capturing the bid-ask spread on rapid inventory turnover.

---

Caveats & known limitations

This is a backtest, and an honest one. Before quoting any number externally:

• No maker fees/rebates modelled. Coincall maker fees are small; if the schedule includes a rebate, the reported PnL is a lower bound.
• Funding rate hard-zeroed. The reservation-price term (γσ² + f) and the per-step accrual are implemented, but f = 0 and no funding feed is wired in.
• No queue-position model. Any fill at a touched price is assumed to be ours — optimistic. Do not size up until this exists.
• Stale-quote fills (≈ 49% at vol_budget=0.5). At tight spreads, roughly half of fills occur when our quote drifts 1–2 ticks past the market touch. In a real LOB these are price-improved (better prices for us), not rejected. The simulation charges us our quoted price, making reported PnL a lower bound.
• OB mid used as reference, not mark/index price.

---

Repository layout

Path	Contents
src/as_model.hpp	Reservation-price + half-spread math (ASParams)
src/intensity.{hpp,cpp}	Roll volatility, intensity MLE (NLopt L-BFGS), fill distances
src/data_reader.{hpp,cpp}	DuckDB glob loader for OB snapshots + trades
src/fill_engine.{hpp,cpp}	Tick loop, quote posting, inventory guards, glitch filter
src/walk_forward.{hpp,cpp}	Rolling window orchestration, no-lookahead firewall
src/results_writer.{hpp,cpp}	CSV + summary emission
src/main.cpp	CLI → config → driver
tests/test_main.cpp	Unit tests (run_tests)
docs/	Design notes, results analysis, and the full handoff

---

Background & citations

1. M. Avellaneda and S. Stoikov (2008). High-frequency trading in a limit order book. Quantitative Finance, 8(3), 217–224. — the original reservation-price / optimal-spread formulation this engine implements.
2. O. Guéant, C.-A. Lehalle, and J. Fernández-Tapia (2013). Dealing with the inventory risk: a solution to the market making problem. Mathematics and Financial Economics, 7(4), 477–507. — the infinite-horizon stationary limit used here to replace T − t for no-expiry perpetuals.
3. R. Roll (1984). A simple implicit measure of the effective bid-ask spread in an efficient market. Journal of Finance, 39(4), 1127–1139. — the serial-covariance volatility estimator used for per-snapshot σ.

---

License

Released under the MIT License.