Latency Arbitrage Defensive Order Sizing

When to Use

Use this skill when a passive, liquidity-providing quote rests on a venue that is slower to reach than the venue where price discovery actually happens — a Nasdaq SPY quote against CME ES, a secondary listing against the primary, a regional venue against the consolidated tape. When the lead venue moves, faster participants race your cancel with an aggressive order against the now-stale quote. Budish, Cramton & Shim (2015) model this directly: the fundamental value follows a compound Poisson jump process, a resting quote is snipe-able only when a jump exceeds half the spread, and the liquidity provider loses the resulting race with probability $\frac{N-1}{N}$ against $N-1$ snipers.

This module answers one narrow question — how much size should be showing given that race — and returns a defensive quantity, a spread multiplier, an already-widened spread, and a cancel directive:

$$P_{\text{snipe}} = 1 - e^{-h \Delta\tau}, \quad h = \lambda \sigma, \qquad Q_{\text{def}} = \left\lfloor Q_0 (1 - P_{\text{snipe}}) \right\rfloor_{\text{lot}}, \qquad W = 1 + 2 P_{\text{snipe}}$$

When NOT to Use

With the shipped lambda_scaling = 0.50 unchanged. It is a placeholder, not a calibrated or published value, and its units are the unusual "snipe-able events per millisecond per unit of annualized volatility". At that default the engine stops quoting entirely above 6.93 ms at $\sigma = 0.20$ and above 1.73 ms at $\sigma = 0.80$ — on a venue with a 3 ms cancel path it would never quote a volatile name. Calibrate against realized markouts on your own passive fills; see adverse-selection-measurement-for-passive-orders.
As a derivation of sniping probability from volatility. It is not one. At 20% annualized volatility a 1 ms window carries a diffusive standard deviation of about 0.026 bps, which puts a 1 bp half-spread roughly 38σ away. The shipped 9.5% cannot come from a diffusion — sniping is a jump phenomenon, which is exactly BCS's point. $\lambda\sigma$ is a monotone proxy for the BCS intensity $\lambda_{\text{jump}}\Pr(J > s/2)$, not a derivation of it.
As a registered market maker's licence to stop quoting. Under MiFID II RTS 8 (Reg. (EU) 2017/578) Art. 1(1), a firm inside a market making agreement must post firm, simultaneous two-way quotes of comparable size and competitive prices for at least 50% of the daily trading hours of continuous trading. Art. 3's exhaustive exceptional-circumstances list does not include "the sizing engine scored elevated sniping risk". A routine defensive pull is not an Art. 3 event.
On one side of a two-sided quote without checking divergence. Art. 1(2)(c) defines quotes as "of comparable size" only where "their sizes do not diverge by more than 50% from each other". Shrinking one side by $P_{\text{snipe}}$ while the other stands unscaled breaches that once the divergence passes 50% — the engine reports size_divergence_ratio and breaches_comparable_size_one_sided so the caller can see it, but it sizes one quote and cannot enforce two-sided parity itself.
As a cancel-race model. This module conditions on losing the race; it has no cancel-vs-sweep margin, no lead-venue imbalance, no clock-domain reconciliation. For the race itself, use cross-venue-latency-arbitrage-defensive-design.
With a mean latency as the input. Pick-off risk lives in the tail of the latency distribution. A gap that averages 2 ms and reaches 20 ms at the 99th percentile is a 20 ms problem — feed a measured high percentile. See latency-monitoring-percentile-based-slas.
As an order router. It returns directives. It never sends, amends, or cancels an order.

Prerequisites

A measured cross-venue exposure window latency_gap_ms — lead-event-to-sweep minus your cancel's delivery time, from one synchronized clock domain, taken at a high percentile rather than the mean.
volatility_annualized for the instrument, and a baseline spread_bps.
min_lot_size set to the instrument's actual round lot. For NMS stocks this is price-tiered, not a flat 100: 100 / 40 / 10 / 1 shares by prior-Evaluation-Period average closing price (17 CFR 242.600(b)(93)). Use round_lot_for_nms_price(); the shipped default of 100 is correct only at or below $250.00 per share.
lambda_scaling calibrated from realized passive-fill toxicity — not inherited from the default.

Workflow

Reject unusable telemetry before it reaches the arithmetic:
- A non-finite latency_gap_ms or volatility_annualized, or a negative volatility, returns INVALID_INPUT_CANCEL at $P_{\text{snipe}} = 1.0$ with the quote pulled. Decision point: the engine fails closed. A defensive sizer that reads a dropped latency probe as "no risk" posts maximum size into exactly the degraded condition it exists to detect.
- A negative gap is not an error — it means your cancel beats the sweep, so exposure is genuinely zero and the full base size stands.
- Structural inputs (base_quote_qty, min_lot_size, lot_increment, spread_bps, symbol) raise ValueError on construction instead. Those are configuration errors, not runtime market conditions, and should surface loudly rather than as a cancel.
Score the sniping hazard:
- $h = \lambda \sigma$ events/ms; $P_{\text{snipe}} = 1 - e^{-h\Delta\tau}$, reported to 4 dp. Rounding is applied before the cancel threshold is tested, which can only ever move a borderline case toward cancelling.
Size, floor, and widen:
- $Q_{\text{def}} = \lfloor Q_0 (1 - P_{\text{snipe}}) \rfloor$, then floored again to a multiple of lot_increment. Decision point: down, never up — rounding a defensive size up shows more risk than the model just authorised.
- $W = 1 + 2P_{\text{snipe}}$, and defensive_spread_bps $= $ spread_bps $\times W$ is returned already applied. Note the model's own gap: $P_{\text{snipe}}$ is spread-independent, so widening does not feed back into it. In BCS a wider spread lowers $\Pr(J > s/2)$ and so lowers the risk directly; here $W$ is a directive to the quoter, not a risk reduction this engine has already banked.
Apply the cancel precedence, highest first — each stage returns a full report so the decision stays auditable:
- INVALID_INPUT_CANCEL → HIGH_SNIPING_RISK_CANCEL ($P_{\text{snipe}} \ge$ threshold, inclusive: at the point of indifference the safe answer is not being on the book) → MIN_LOT_CANCEL (a sub-round-lot residual pays the fee without holding a usable quote, and on an NMS stock it is odd-lot information under Rule 600(b)(69) rather than a protected quotation) → QUOTE_DEFENSIVELY_SIZED.
Check the size divergence before sending:
- size_divergence_ratio measures the reduction against the smaller quote — the conservative reading, since Art. 1(2)(c) does not name a denominator. A pulled quote reports inf, not a small number.

Full procedure: see references/workflows.md. Standards reference: see references/standards.md. Printable pre-flight checklist: see assets/checklist.md.

Common Pitfalls

Failing open on degraded telemetry. A NaN latency sample does not compare greater than zero, and max(0.0, nan) is 0.0 — so a naive implementation scores 0% sniping risk and posts the full quote. This engine's single worst failure mode is silently treating "I cannot measure the gap" as "there is no gap".
Inheriting lambda_scaling. No venue, regulator, or paper publishes this constant. Shipping the default into production sets your quoting cut-off at an arbitrary latency you did not choose.
Reading $P_{\text{snipe}}$ as a calibrated probability. It is an ordinal risk score built on a proxy hazard. Do not price options off it, and do not report it to a risk committee as a probability of being picked off.
Shrinking one side of a two-sided quote. Under a market making agreement, sizes that diverge by more than 50% are no longer "of comparable size" (RTS 8 Art. 1(2)(c)). The defensive reduction that protects you from sniping is the same reduction that breaches the agreement.
Treating a defensive pull as an Art. 3 exceptional circumstance. Art. 3 lists extreme volatility triggering volatility mechanisms; war, industrial action, civil unrest, cyber sabotage; disorderly trading conditions; inability to maintain prudent risk management; and non-equity suspensions. Elevated sniping risk is on none of those lists. (A genuinely broken data feed may fall under Art. 3(d)(i) — routine elevated latency does not.)
Hard-coding a 100-share minimum. On a $1,500 stock the NMS round lot is 10 shares, so a valid 40-share defensive quote is cancelled by the default for no reason.
Posting static size through a latency spike. Holding a 10,000-share passive quote while the cross-venue gap widens to 20 ms is the failure this skill exists to prevent — but note that at the shipped defaults the engine reaches full cancellation long before 20 ms, so verify your calibrated cut-off is where you intend it.
Feeding a mean latency. The gap that picks you off is the tail one.

Verification

Normal market. MarketStateSpec("AAPL", 1000, latency_gap_ms=1.0, volatility_annualized=0.20, spread_bps=2.0, min_lot_size=100) $\implies$ $h = 0.10$/ms, $P_{\text{snipe}} = 1 - e^{-0.1} = 0.0952$, defensive_quote_qty = 904 (floored from 904.8, not 905), $W = 1.19$, defensive_spread_bps = 2.38, size_divergence_ratio $= 96/904 \approx 0.106$, no comparable-size breach, QUOTE_DEFENSIVELY_SIZED.
High latency, volatile. $\Delta\tau = 25$ ms, $\sigma = 0.80$ $\implies$ exponent $-10$, $P_{\text{snipe}}$ rounds to $1.0$, defensive_quote_qty = 0, size_divergence_ratio = inf, HIGH_SNIPING_RISK_CANCEL.
Threshold is inclusive. $\Delta\tau = \ln 2 / 0.10 = 6.931$ ms at $\sigma = 0.20$ puts $P_{\text{snipe}}$ at exactly $0.50$ $\implies$ must cancel, not quote.
Fails closed. latency_gap_ms = float("nan") on a 10,000-share base $\implies$ INVALID_INPUT_CANCEL, defensive_quote_qty = 0, $P_{\text{snipe}} = 1.0$. It must not return QUOTE_DEFENSIVELY_SIZED with 10,000 shares.
Round lot is price-tiered. round_lot_for_nms_price(250.00) == 100, (250.01) == 40, (1000.01) == 10, (10000.01) == 1.
Run python -m unittest discover -s skills/latency-arbitrage-defensive-order-sizing/scripts.

Latency Arbitrage Defensive Order Sizing

When to Use

When NOT to Use

Prerequisites

Workflow

Common Pitfalls

Verification

Hands off to 7

Handed off from 3

When to Use

When NOT to Use

Prerequisites

Workflow

Common Pitfalls

Verification

Related Skills

Hands off to 7

Handed off from 3