Wholesale Credit
Risk Engine.

Everything here follows from one fact.

A wholesale credit book is a low-default portfolio. This one defaults at 1.20% a year: 692 events in 229,803 obligor-quarters, and only 136 out of time. The single most useful thing to internalise about PD modelling is that the effective sample size is the number of defaults, not the number of rows. Almost every technique on this page is a response to having very few events.

Real macro, synthetic obligors.

Four series are pulled live from FRED and collapsed into a single standardised credit-cycle index Z (higher = worse). Equal weights on the sign-oriented standardised series — deliberately not a fitted PCA, because fitted weights on 64 quarterly observations would be close to pure noise. If no API key is present, each series falls back to a calibrated synthetic analogue and the mode used is reported per-series in the console, in the figure below, and in the model document header.

Two data traps, both easy to miss

• The obvious BBB spread series, BAMLC0A4CBBB, only carries about three years of history on FRED — useless for a 2010–2025 panel. Replaced with BAA10Y (Moody's Baa less the 10-year Treasury), daily from 1986.
• COMREPUSQ159N is already published as a year-on-year growth rate. Differencing it again produced values in the hundreds of percent. Caught by looking at the raw series rather than trusting the series name.

How defaults are generated

A one-factor Merton/Vasicek latent-variable model. An obligor defaults when its latent asset index crosses a threshold:

One judgement call worth defending

The real macro stress index hits +4.1σ in 2020Q2. Fed straight into a Vasicek model, that implies a quarterly default rate around 10% — roughly 40% annualised. That is not what happened. Corporate default rates in 2020 rose to a few multiples of normal, not forty, largely because policy support broke the historical macro-to-default relationship. The factor is therefore tanh-squashed: linear through the ordinary range, compressed in the tail. 2020 and the 2010–11 hangover remain clearly the worst periods in the sample, at roughly 3× the long-run rate.

Weight of Evidence, then Firth.

Each continuous driver is binned, and each bin gets WoE = ln(%non‑default / %default), so a higher WoE means safer. Binning linearises a non-linear driver-to-log-odds relationship without letting the model invent an arbitrary shape; it is robust to the outliers that dominate financial ratios (a 40× leverage observation stops being a leverage point); and it makes the scorecard readable, because every rating decomposes additively into a per-driver contribution a credit officer can challenge.

The bit most implementations get wrong

Bins need a minimum number of defaults, not just a minimum number of observations. Without that constraint, quantile seeding leaves bins holding zero or one default; the smoothed WoE for such a bin is an artefact of the smoothing constant rather than an estimate, and Information Value comes out inflated by an order of magnitude. My first run produced IVs of 6.4 — that was the bug, and tying the minimum to a fraction of the total default count rather than the observation count is what fixes it.

The top three exceed 0.50, and by convention that is a leakage warning. Worth saying before anyone else does: here it is an artefact of the synthetic process, because the ratios literally generate the latent default index, so their relationship to default is cleaner than any real accounting ratio's would be. Note also that IV is a univariate screen and does not add up across correlated drivers — which is why individual IVs near 0.7 sit comfortably alongside a portfolio Gini of 0.59.

Champion: Firth-penalised logistic regression

Firth adds a Jeffreys-prior penalty +½·log|I(β)| to the log-likelihood. Ordinary maximum-likelihood logistic regression is biased away from zero in rare-event samples and — the property that actually matters operationally — is not guaranteed to produce finite estimates under quasi-complete separation. On a low-default book, the first time you cut the sample by sector or vintage and hit a cell with no defaults, plain MLE diverges. A model that silently blows up on a thin sector cut cannot be run in production. Implemented from scratch by modified-score iteration.

Out of time, never random

Grade 1 has zero defaults. Now what?

The score is cut into 10 grades on the development sample, and the cut points are then frozen and applied unchanged out of time — re-cutting on the test sample would conceal exactly the migration the PSI diagnostic exists to detect. The masterscale is deliberately not equal-population: fine at the safe end, coarse at the distressed end, like the S&P and Moody's scales. That is where rating decisions are made, and it means the safest grades carry few or zero defaults — the problem to handle, rather than hide.

Grade 1 in this run holds 3,083 obligor-quarters and not one default. A naive d/n assigns PD = 0, and therefore zero capital and zero allowance. A zero is not an estimate; it is an absence of evidence.

The interval, not the point estimate.

Out-of-time Gini 0.587, against a development Gini of 0.562 — so discrimination does not decay out of time. But the headline number is the 95% confidence interval: [0.513, 0.657], width 0.144.

Stability

PSI on the score distribution and CSI per driver, development versus out-of-time, against the standard 0.10 amber / 0.25 red thresholds. Bins are cut on the development distribution and reused for the test sample — cutting separately returns approximately zero by construction, which is a real and common bug.

Champion versus challenger

The logistic is retained as champion. Three reasons, in order of weight:

1. The difference does not survive sampling uncertainty. Paired bootstrap of the Gini difference: −0.026, 95% CI [−0.056, +0.002] — not distinguishable from zero. Promoting a challenger on a difference the data cannot resolve is model risk, not model improvement.
2. Governance explainability. Six coefficients on monotone, policy-signed WoE bins. Every rating movement decomposes additively into a per-driver contribution. The challenger requires post-hoc attribution, which is an explanation of an explanation.
3. Gradient boosting cannot extrapolate. Tree ensembles are piecewise constant: outside the training range of a driver, the prediction is flat. In stress testing the entire question is what happens when drivers move beyond anything in the training window. A model structurally incapable of responding to that is disqualified for the use case, whatever its in-sample discrimination.

Reason 3 is the one that ends the argument, and it is specific to stress testing.

Bounded, bimodal, and drawn down.

LGD is estimated with a fractional-response GLM — binomial family, logit link, quasi-maximum likelihood (Papke–Wooldridge), with HC0 heteroskedasticity-robust standard errors. The robust covariance is not optional: under QMLE the model's own information-matrix standard errors are inconsistent.

Downturn LGD is the same model evaluated with the macro stress term at its 95th historical percentile, holding facility characteristics fixed — the Basel "downturn conditions" idea without inventing a separate dataset.

EAD = drawn + CCF × undrawn

The regulatory question is how much of an undrawn commitment a borrower pulls down on the way to default. Estimated CCF is 0.519 for revolvers and 0.302 for term loans — but the operative result is the gradient across obligor deterioration.

Obligors heading toward default draw on committed lines while they still can. A single portfolio-average CCF therefore understates EAD precisely in the states of the world where EAD matters. That sentence is the whole point of the module.

CCAR and CECL are not the same question.

PD is conditioned on the macro state through the Vasicek single-factor transform, PD(Z) = Φ( (Φ⁻¹(PDttc) + √ρ·Z) / √(1−ρ) ). The asset correlation is moment-matched from the historical default-rate series (unconstrained estimate 0.083) and then bounded to the Basel corporate range, giving ρ = 0.12. The bridge from a supervisory macro path to Z is a four-variable OLS regression, R² = 0.66 — an ordering device, not a forecasting model.

A model document that cannot drift.

The model document is generated from the run, not written by hand, so it can never fall out of step with the model. Its header stamps the semantic version, the git commit, the run timestamp and a SHA‑256 hash of the input data — change any input and the hash changes and the document changes with it. It is framed against SR 11‑7, the Fed/OCC supervisory guidance on model risk management. Two sections carry the weight.

§7 Limitations — deliberately blunt

• The obligor portfolio is synthetic, generated by a process close to the fitted form. Measured performance is an upper bound on what the same specification would achieve on real data.
• 692 defaults in total, 136 out of time. Every statistic downstream inherits that sample size.
• The out-of-time Gini interval spans 0.513 to 0.657. Any comparison turning on a difference smaller than that width is not supported by this sample.
• One realised cycle. The macro-to-Z regression has four parameters on 64 quarterly observations, and should be treated as an ordering device rather than a forecasting model.
• No qualitative overlay. Production rating systems apply analyst judgement, watchlist status, parent support and covenant breaches on top of the statistical score. None of that is here.
• No out-of-time validation of LGD or CCF. Both are estimated on the pooled defaulted population; there are too few defaults to hold out a time window and retain a usable sample. A genuine gap, not a simplification.
• Asset correlation is bounded, not freely estimated. The unconstrained estimate is 0.083 and was clipped into the Basel range. The clip is a judgement call and it moves the scenario losses.

§8 Monitoring thresholds — pre-committed

These are committed at development, before any monitoring result is observed. That ordering is the entire point: a threshold chosen after seeing the outcome is not a control.

Cadence: PSI and CSI monthly; discrimination and calibration quarterly on a rolling four-quarter window; full revalidation annually or immediately on any red breach. Escalation at red is written notification to model risk management within five business days, with a remediation plan and an interim compensating control — typically a conservative PD floor or an override requirement — in place until remediation completes.

Under 60 seconds, bit-reproducible.

The whole pipeline runs end to end in about 25 seconds warm and 37 seconds cold, on numpy, pandas, scikit-learn, statsmodels and matplotlib. No xgboost — the challenger is sklearn's HistGradientBoostingClassifier. Every stochastic component derives from one master seed via fixed per-module offsets, so adding a module cannot perturb an earlier module's draws.

The FRED key is read from the FRED_API_KEY environment variable and is never written to disk or committed; responses are cached locally so reruns skip the network. Without a key, every series falls back to a calibrated synthetic analogue and the mode used is reported per-series in the console, in Fig. 2, and in the model document header. You are never left guessing which data produced the numbers.

License: MIT. Synthetic data throughout except the FRED macro series. Not investment advice, and not a validated production credit model — see §1 and §7 of the model document for intended use and limitations.