Order-Book Entropy + Cancel-Shock Slippage Early-Warning Playbook

Date: 2026-02-26
Category: Research (Execution / Slippage Modeling)
Scope: Intraday equity execution (KR-focused, but portable)

Why this model exists

Most slippage controllers react too late.

They usually wait for one of these to happen:

• realized spread widening,
• markout deterioration,
• repeated passive misses,
• or quote fade already visible in top-of-book.

By then, the order is often already paying the tax.

This playbook builds an early-warning layer for slippage using two leading signals:

1. Order-book entropy collapse (depth becomes concentrated/fragile),
2. Cancel shock bursts (visible liquidity evaporates faster than normal replenishment).

Core idea: treat displayed liquidity as perishable inventory. When structure fragility appears before price moves, execution mode should de-risk preemptively.

Conceptual model

We define a latent state variable:

[ S_t \in {\text{Stable}, \text{Fragile}, \text{Toxic}} ]

State transitions are driven by:

• microstructure stress features (entropy, cancellation pressure, imbalance acceleration),
• short-horizon volatility and spread drift,
• local fill-hazard deterioration.

The controller maps state to execution policy:

• Stable → passive-first, queue improvement allowed.
• Fragile → reduce quote persistence, tighten participation caps, avoid overexposure at stale levels.
• Toxic → protect tail (q95/CVaR), prioritize completion certainty over rebate theater.

Signal design

1) Order-book entropy

For each side (bid/ask), take top (L) levels with normalized depth weights:

[ p_{i,t}^{(side)} = \frac{q_{i,t}^{(side)}}{\sum_{j=1}^{L} q_{j,t}^{(side)}} ]

Shannon entropy:

[ H_t^{(side)} = -\sum_{i=1}^{L} p_{i,t}^{(side)} \log p_{i,t}^{(side)} ]

Interpretation:

• High entropy: depth is distributed across levels (more robust shape).
• Low entropy: depth concentrated in few levels (more brittle to cancellations/sweeps).

Use an intraday z-score by symbol-time bucket:

[ Z^H_t = \frac{H_t - \mu_{H, bucket}}{\sigma_{H, bucket}} ]

Focus on entropy drop velocity as an early warning:

[ \Delta H_t^{(k)} = H_t - H_{t-k} ]

Large negative (\Delta H) often precedes slippage bursts.

2) Cancel shock index (CSI)

Define per-window cancel and add flow (message-level or L2 diff based):

• (C_t): canceled displayed volume,
• (A_t): newly added displayed volume,
• (T_t): traded (executed) volume.

A robust shock statistic:

[ CSI_t = \frac{C_t - \lambda A_t}{\epsilon + T_t + \eta A_t} ]

with tuned (\lambda, \eta) to discount healthy replenishment.

Then standardize by bucketed history:

[ Z^{CSI}t = \frac{CSI_t - \mu{CSI,bucket}}{\sigma_{CSI,bucket}} ]

A high positive (Z^{CSI}) means liquidity is being withdrawn disproportionately fast.

3) Coupled fragility score

Construct a composite score:

[ F_t = w_1(-Z^H_t) + w_2 Z^{CSI}t + w_3 |\Delta I_t| + w_4 \Delta s_t + w_5 \hat{\sigma}{short,t} ]

where:

• (\Delta I_t): imbalance acceleration,
• (\Delta s_t): spread widening speed,
• (\hat{\sigma}_{short,t}): short-horizon realized volatility proxy.

This score is a feature (not final decision). Final state should be produced by a probabilistic model.

Modeling stack

A. State classifier (fast path)

Train a 3-class model for (S_t):

• LightGBM/CatBoost for tabular low-latency inference,
• class-balanced focal loss to emphasize rare toxic windows,
• probability calibration (temperature scaling or isotonic).

Output:

[ P_t = \big(P(Stable), P(Fragile), P(Toxic)\big) ]

B. Tail slippage model (risk path)

Separately model conditional tail cost (e.g., next 30-120s expected IS quantiles):

• quantile regression (q50/q90/q95),
• optional EVT tail fit above high threshold for stress windows.

This path gives the controller risk budget updates.

C. Transition smoothing

Avoid mode flapping with a sticky transition filter:

• Hidden Markov smoothing or
• explicit hysteresis rules on calibrated probabilities.

Example:

• enter Toxic if (P(Toxic)>0.62) for 2 consecutive windows,
• exit Toxic only if (P(Toxic)<0.40) for 3 windows.

Labeling strategy

Define slippage target relative to decision/arrival benchmark:

[ Y_{t,h} = \text{IS}_{t \to t+h} \quad (h \in {30s, 60s, 180s}) ]

Label regimes from forward outcomes + local microstructure context:

• Stable: low tail slippage and normal fill hazard,
• Fragile: moderate deterioration, elevated cancellation pressure,
• Toxic: top-decile (or stricter) forward slippage and/or severe fill collapse.

Important: use purged temporal splits to avoid leakage from overlapping horizons.

Online controller

Let (B_t) be remaining slippage budget (bps) for the parent order.

Policy template

1. Infer state probabilities and tail forecasts every (\Delta) seconds.
2. Update expected budget burn:

[ \hat{b}t = f\big(P_t, \hat{q95}{slip,t}, participation_t\big) ]

3. Map to action mode:

• Mode A (Stable)

  • passive skew enabled,
  • wider patience timeout,
  • normal participation ceiling.

• Mode B (Fragile)

  • reduce passive dwell time,
  • tighter cancellation/replace thresholds,
  • cap participation ramp rate.

• Mode C (Toxic)

  • prioritize certainty and inventory-risk reduction,
  • hard cap on quote lifetime,
  • optional venue quarantine if cancel shock is venue-local,
  • invoke "tail guard" when projected budget breach probability exceeds threshold.

4. If projected (B_t) breach risk > limit, force defensive completion protocol.

Feature table (production minimum)

• Entropy features:
  • bid/ask entropy level and slope,
  • entropy asymmetry,
  • entropy recovery half-life after shock.
• Cancel dynamics:
  • cancel/add ratio,
  • CSI z-score,
  • burst duration and inter-burst interval.
• Book/price coupling:
  • microprice drift,
  • spread speed,
  • imbalance acceleration.
• Execution context:
  • own participation rate,
  • queue-age of resting orders,
  • recent fill hazard and reject rate.
• Session controls:
  • open/close auction proximity,
  • lunch/low-liquidity bucket,
  • venue/session state (KRX/NXT/VI guard).

Evaluation framework

Offline

• Primary: q95 IS reduction vs baseline schedule/router.
• Secondary:
  • fill shortfall,
  • opportunity-cost drift,
  • mode-switch frequency (stability metric),
  • calibration error of (P(Toxic)).

Use block bootstrap by day and symbol cohort.

Shadow/live

• Run controller in shadow first (decision logging only),
• compare counterfactual actions via replay where possible,
• then staged capital rollout:
  • phase 1: low ADV names excluded,
  • phase 2: medium liquidity,
  • phase 3: full universe with guardrails.

Hard stop triggers:

• toxic false-negative spike,
• mode-flap explosion,
• unexplained underfill > threshold.

Drift & reliability guards

• Population stability index for key features (entropy, CSI).
• Probability calibration monitor by session bucket.
• Feature-latency SLO: stale feature stream automatically degrades to safe fallback policy.
• Fallback policy must be explicit, deterministic, and tested.

If entropy input is delayed or malformed, do not keep using stale fragility scores.

Practical implementation notes

• Compute entropy from a fixed level depth tensor (e.g., top 5 or top 10); avoid variable-level artifacts.
• Bucket normalization by symbol + time-of-day is mandatory (open/close dynamics differ materially).
• Exclude auction-cross prints from continuous-book feature windows unless intentionally modeled.
• For KR deployment, align with KRX/NXT session boundaries and VI states before acting on signals.

Pseudocode

for each decision_tick t:
    x_t = build_features(book, trades, cancels, adds, own_exec)
    p_state = clf.predict_proba(x_t)  # stable/fragile/toxic
    q95 = tail_model.predict_quantile(x_t, q=0.95)

    state = hysteresis_filter.update(p_state)
    burn = burn_model(state, q95, participation, remain_qty)

    if breach_prob(slippage_budget, burn) > TH_BREACH:
        mode = "TOXIC_DEFENSIVE"
    else:
        mode = policy_map(state)

    action = execution_policy(mode, market_state, remain_qty)
    send(action)

What this improves (if done right)

• Lower p95 slippage in cancellation-driven stress windows,
• fewer late panic transitions,
• better distinction between temporary noise and genuine liquidity withdrawal,
• clearer operator diagnostics ("why did we switch mode?").

This is not a magic predictor. It is a risk-aware timing layer that moves decisions earlier, when adaptation is still cheap.

Next experiments

1. Venue-local CSI decomposition to isolate one-venue liquidity failures.
2. Cross-impact extension for portfolio baskets (fragility contagion across names).
3. Conformal risk envelope around toxic probability for stronger online coverage guarantees.
4. Joint optimization of slippage tail + underfill penalty via constrained MPC.

One-line takeaway

If your slippage model only reacts after spread and markout already blow out, you are paying tuition; entropy collapse + cancel shocks let you switch regimes before the bill arrives.