Off-Exchange Internalization and Lit Residual Toxicity: A Slippage Modeling Playbook

Date: 2026-03-09
Category: research (execution microstructure)

Why this matters

When benign retail flow is heavily internalized off-exchange, displayed lit liquidity can become a selection-biased remainder:

• quotes still look tight,
• spread capture looks tempting,
• but fills on lit books become increasingly toxic,
• and passive strategies pay through post-fill markouts.

So the desk is not just routing across venues. It is routing across different information pools.

Failure pattern (seen in production)

1. Router sees stable NBBO and healthy displayed depth.
2. Passive lit posting is increased to harvest spread/rebates.
3. Benign contra flow gets internalized elsewhere first.
4. Lit fills arrive disproportionately when informed flow sweeps through.
5. Short-horizon markouts worsen; queue alpha goes negative.
6. Model still attributes losses to “volatility/noise” instead of venue-flow selection.

Net effect: apparent spread quality masks worsening adverse selection.

Mechanism in one equation

Let

• (\lambda_B): benign contra-arrival intensity
• (\lambda_T): toxic contra-arrival intensity
• (p_B): probability benign flow is absorbed off-exchange
• (p_T): probability toxic flow is absorbed off-exchange

Then toxic share among lit fills is

[ \tau_{lit}=\frac{(1-p_T)\lambda_T}{(1-p_B)\lambda_B + (1-p_T)\lambda_T} ]

If (p_B > p_T) (common in practice), (\tau_{lit}) rises even when headline spread is unchanged.

That is the residual-toxicity channel.

Cost decomposition

For parent notional (Q):

[ C_{total}=C_{px}+C_{fee}+C_{markout}+C_{delay}+C_{catchup} ]

where

• (C_{px}): immediate execution vs benchmark
• (C_{fee}): maker/taker + routing economics
• (C_{markout}): adverse post-fill drift (core residual-toxicity cost)
• (C_{delay}): waiting cost if passive policy underfills
• (C_{catchup}): late aggressive completion cost

In this regime, (C_{markout}) dominates long-run leakage.

Core signals (add to dashboard)

1. Off-Exchange Absorption Skew (OEAS)
   Estimated differential absorption of benign vs toxic flow (proxy for (p_B-p_T)).

2. Lit Residual Toxicity Index (LRTI)
   Difference between realized lit-fill markout and blended-venue baseline markout.

3. Quote-to-Print Dissociation (QPD)
   Frequency of stable quotes but unstable execution outcomes/markouts.

4. Passive Edge Decay (PED)
   Rolling decay of expected passive edge: spread+rebate minus expected markout.

5. Residual Completion Pressure (RCP)
   Risk that conservative posting now forces expensive catch-up later.

Modeling architecture

1) Two-layer fill model

Layer A: fill probability by venue/policy.
Layer B: conditional markout distribution given fill.

Do not collapse these into one average-cost model. Separation is required to expose selection effects.

2) Branch model per child decision

For each action (lit post / midpoint / take):

• branch 1: fill + favorable markout
• branch 2: fill + adverse markout
• branch 3: no fill + queue decay
• branch 4: forced aggressive catch-up

Optimize expected cost with tail penalty:

[ J(a)=\mathbb{E}[C_{total}|x_t,a] + \lambda,\text{CVaR}{95}(C{total}|x_t,a) ]

3) Regime feature set

• off-exchange share by symbol/time bucket
• microprice drift and OFI
• queue depletion velocity
• lit-vs-off-ex trade-size mix
• rolling markout asymmetry (buy vs sell)

Practical state controller

• STATE A: BALANCED FLOW
  LRTI low, PED stable → normal passive mix.

• STATE B: BENIGN-DRAIN
  OEAS rising, passive fill quality degrading → reduce lit passive dwell time, increase conditional midpoint probing.

• STATE C: LIT-TOXIC
  LRTI high, markout tails widening → downweight lit passive; prioritize faster completion paths with tighter risk caps.

• STATE D: SAFE MODE
  Tail budget breached or completion at risk → enforce conservative participation cap + deterministic fallback rules.

Use hysteresis to avoid rapid mode flapping.

Guardrails for live deployment

1. Markout-first venue scoring
   Score venues by net post-fill outcome, not quoted spread alone.

2. Passive-edge kill switch
   If PED < 0 beyond threshold window, auto-throttle passive posting.

3. Time-left residual cap
   Prevent late forced catches by explicit residual budget checkpoints.

4. Symbol-bucket segmentation
   Internalization effects vary by symbol/price/retail intensity; avoid global policy.

5. Counterfactual replay lane
   Daily replay current policy vs toxicity-aware policy before expanding rollout.

Minimal rollout checklist

• Add OEAS/LRTI/PED/RCP telemetry to execution dashboard
• Split fill model from post-fill markout model in training pipeline
• Add CVaR95 objective and state-machine action map
• Enable passive-edge kill switch and residual checkpoints
• Run 2-week shadow A/B by symbol buckets
• Promote only if completion stays stable and q95 net slippage improves

Bottom line

Off-exchange internalization can quietly transform lit books into a more toxic residual pool.
If your slippage model ignores that selection effect, passive fills look cheap until markouts and late catch-up costs settle the bill.