Execution Cost Model Recalibration Cadence

When to Use

Use this skill in quantitative execution research, Transaction Cost Analysis (TCA), and portfolio construction where a pre-trade cost model feeds sizing, venue selection, or algo parameter choice. The audited model is the standard two-term decomposition

$$\text{IS}{\text{pred}} = \eta \cdot \text{Spread}{\text{bps}} + \gamma \cdot \sigma_{\text{bps}} \cdot \sqrt{\text{Qty} / \text{ADV}}$$

whose second term is the square-root impact law $I(Q) = Y \sigma \sqrt{Q/V}$ with $Y \sim 0.5\text{–}1.0$ (Tóth et al. 2011; Almgren et al. 2005). As market regimes shift — volatility spikes, tick-size regime changes, fee-schedule updates, venue mix changes — the fitted coefficients go stale, and the model develops tracking error ($\text{RMSE}$) and systematic bias ($\bar{\epsilon} \ne 0$) against realized IS. This module implements the trigger arm of a recalibration cadence: measure the drift, decide whether it warrants a refit, and produce refitted coefficients only when the sample can actually support them.

When NOT to Use

• As the whole cadence. This is the trigger arm only. The calendar arm — the scheduled weekly/monthly review, and the annual validation floor RTS 6 Art. 9 places on EU algorithmic trading firms — is a scheduler concern and is not implemented here.
• To promote parameters straight to production. The refit is scored in-sample, on the very trades that triggered it. post_refit_rmse_bps is an optimistic lower bound on live tracking error, not a forecast of it. Validate on a held-out or subsequent sample first.
• To diagnose why the model drifted. A tripped threshold is a symptom. If the error came from a venue outage, a fee change, or a handful of outlier parents, refitting bakes that event into $\eta$ and $\gamma$. Screen the sample before refitting; use execution-slippage-attribution-timing-vs-sizing to decompose where the shortfall actually came from.
• On a sample that does not span order sizes and spread regimes. If every trade has near-identical spread and participation, the two regressors are collinear and $\eta$ and $\gamma$ are not separately identifiable — the combined prediction can look fine while each coefficient is arbitrary. The engine refuses such a fit rather than returning it.
• On incomplete executions. The engine treats its input as an unordered sample of completed parent orders. Working or partially-filled orders leak incomplete outcomes into the fit.
• As an optimal-execution scheduler. This calibrates a cost estimate; it does not produce a trade schedule. For the schedule, see execution-algo-twap-vwap-slicing and implementation-shortfall-minimization.

Prerequisites

• Trade execution history of completed parent orders: order_qty, adv_shares, spread_bps, volatility_daily_pct, realized_is_bps.
• Units contract. The square-root law is dimensionally homogeneous — $\sigma$ must be in the same relative unit as the cost it predicts. This module works in bps, so volatility_daily_pct is percent ($1.5$ means $1.5%$/day) and is converted internally to bps ($\times 100$). Supplying a decimal fraction ($0.015$) understates the impact term by $100\times$.
• Active model parameters ($\eta_{\text{active}}, \gamma_{\text{active}}$).
• Governance configuration: tracking-error limit, bias limit, minimum refit sample size. These are defaults, not industry standards — see references/standards.md.

Workflow

1. Validate the sample before measuring anything.

   • Decision point — reject non-finite values; never let them reach the metrics. A single NaN in realized_is_bps propagates through the mean into both RMSE and bias, and every nan > threshold comparison evaluates False. Unvalidated, corrupt data reports the model as stable and silently suppresses the recalibration it should have triggered.
   • Reject non-positive order_qty and adv_shares (a zero ADV is a division by zero, a negative quantity a domain error on the square root) and implausible daily volatility, which is nearly always a units mistake.

2. Model Performance Audit — compute against the active parameters:

   • Tracking error: $\text{RMSE} = \sqrt{\frac{1}{N} \sum (\text{IS}{\text{realized}} - \text{IS}{\text{predicted}})^2}$
   • Systematic bias: $\bar{\epsilon} = \frac{1}{N} \sum (\text{IS}{\text{realized}} - \text{IS}{\text{predicted}})$, signed so positive means the model under-predicts cost.
   • Decision point — compare thresholds on the unrounded metrics. Rounding to display precision before the comparison creates a dead band: a bias of $+1.502$ bps rounds to $1.50$ and then fails a $|\bar{\epsilon}| > 1.50$ test. Round only when writing the report.

3. Recalibration Trigger Audit: $\text{RMSE} > \text{RMSE}{\max}$ OR $|\bar{\epsilon}| > |\bar{\epsilon}|{\max} \implies$ the model has drifted.

4. Sample-sufficiency gate — a breach is not automatically a refit.

   • Decision point — if $N < N_{\min}$, defer. Emit RECALIBRATION_DEFERRED_INSUFFICIENT_SAMPLE, retain the active parameters, and re-audit when the sample grows. Refitting a two-coefficient model on a handful of trades fits noise, and unstable cost coefficients destabilise every downstream portfolio optimisation that consumes them.

5. Parameter Least-Squares Refitting — solve the no-intercept normal equations in closed form for $$\text{IS}_{\text{realized}} = \eta \cdot \text{Spread} + \gamma \cdot \sigma \cdot \sqrt{\text{Qty}/\text{ADV}}$$

   • No intercept is fitted: a zero-size order in a zero-spread market has zero modelled cost, and a free intercept would absorb size-dependent impact into a constant.
   • The active parameters are not an input to the fit. Least squares finds the sample optimum; seeding it with the incumbent values would only bias the result toward a model the audit has already rejected.
   • Decision point — check the design conditioning before trusting the coefficients. The engine reports $\det/(S_{11}S_{22})$, which equals $1 - \cos^2$ of the angle between the two regressor columns ($1.0$ orthogonal, $0.0$ collinear). Below the floor, escalate to RECALIBRATION_REQUIRED_MANUAL_REVIEW rather than shipping arbitrary coefficients.
   • Decision point — a negative fitted coefficient is not a small number, it is a wrong sign. $\eta < 0$ or $\gamma < 0$ implies wider spreads or larger orders reduce cost. Withhold the recommendation and investigate the sample.

6. Validate before promotion: the report carries post_refit_rmse_bps and post_refit_bias_bps, both in-sample. Treat them as a sanity floor, not evidence the new parameters will hold live. Promote through the same versioning and rollback path as any other model change (model-versioning-and-rollback).

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

Common Pitfalls

• Silently auditing corrupt data: a NaN realized IS makes RMSE and bias NaN, and nan > limit is False on every threshold — so the worst possible data produces the most reassuring verdict, MODEL_PARAMETER_STABLE, and no recalibration is raised. Reject non-finite inputs at ingestion.
• Over-recalibrating on transient noise: refitting daily on a handful of trades produces high parameter variance and unstable portfolio optimisation. Gate the refit on sample size, not just on a threshold breach.
• Rescaling instead of refitting: multiplying both coefficients by a single ratio of mean realized to mean predicted cost cannot separate $\eta$ from $\gamma$ — it preserves whatever ratio the seed had, no matter what the data says, so a pure impact-regime shift silently reprices spread costs as well. A two-regressor least-squares solve is what "refit" has to mean here.
• Mismatched volatility units: the square-root law needs $\sigma$ in the same relative unit as the predicted cost. Feeding a decimal fraction where percent is expected shrinks the impact term $100\times$, making a 10%-of-ADV order look like a sub-bps execution and pushing all the fitted cost into the spread coefficient.
• Ignoring systematic prediction bias: tracking correlation while a constant under-prediction ($\bar{\epsilon} = +4.0$ bps) persists lets portfolio managers systematically underestimate trading costs on every order.
• Trusting an in-sample refit: the refit is scored on the trades that triggered it, so its RMSE is guaranteed no worse than the incumbent's — that is arithmetic, not evidence. Only out-of-sample performance is evidence.
• Refitting through a one-off event: a venue outage or fee-schedule change inflates realized cost for a specific reason. Recalibrating on that window bakes a transient into the standing model.
• Using outdated historical trade windows: training on calm, low-volatility history during a crash regime — or the reverse — produces a model calibrated to a regime that is no longer running.
• Refitting on a sample with no design variation: all-similar orders make the spread and impact regressors collinear; the fit "succeeds", the combined prediction looks reasonable, and each coefficient is individually meaningless.

Verification

• Instantiate ExecutionCostModelRecalibrationEngine() with active parameters $\eta = 0.5$, $\gamma = 1.0$.
• Prediction units: for a 9,000-share order against 100,000 ADV ($\sqrt{0.09} = 0.3$) at a 2.0 bps spread and $1.5%$/day volatility, predict_slippage_bps must return $0.5 \times 2.0 + 1.0 \times 150 \times 0.3 = 46.0$ bps.
• Scenario 1 — stable: 60 trades generated exactly at the active parameters $\implies$ RMSE and bias both $0$, status MODEL_PARAMETER_STABLE, no recommended parameters.
• Scenario 2 — regime shift: 60 trades generated at $\gamma = 2.0$ against an active $\gamma = 1.0$ $\implies$ status RECALIBRATION_RECOMMENDED, positive bias above the limit, and refitted $(\eta^, \gamma^) = (0.5, 2.0)$ recovered exactly.
• Scenario 3 — identifiability: data generated at $(\eta, \gamma) = (0.2, 3.0)$ must refit to that ratio, not to the ratio of whatever seed the fitter started from.
• Scenario 4 — governance gates: the same breach observed over 3 trades $\implies$ RECALIBRATION_DEFERRED_INSUFFICIENT_SAMPLE with no recommended parameters; an all-identical sample $\implies$ RECALIBRATION_REQUIRED_MANUAL_REVIEW on collinearity; a sample fitting to $\eta < 0$ $\implies$ RECALIBRATION_REQUIRED_MANUAL_REVIEW with the recommendation withheld.
• Least-squares property checks: residuals orthogonal to both regressor columns, and post_refit_rmse_bps never exceeding the active RMSE.
• Negative checks: empty history, NaN/inf realized IS, zero or negative ADV, negative quantity, negative spread or volatility, and implausible volatility must each raise.
• Run python -m unittest discover -s skills/execution-cost-model-recalibration-cadence/scripts.

Related Skills

• execution-algo-parameter-optimization-via-backtest
• execution-slippage-attribution-timing-vs-sizing
• transaction-cost-analysis-tca-integration
• model-versioning-and-rollback
• model-staleness-detection