Chapter 15: Key Takeaways — Credit Risk Modelling and Model Risk Management


Core Concepts

The Expected Loss Formula

The foundational equation of credit risk:

$$\boxed{EL = PD \times LGD \times EAD}$$

Component Definition Typical Range (Retail) Typical Range (Corporate)
PD (Probability of Default) Probability borrower defaults within 1 year 0.5%–15% 0.05%–5%
LGD (Loss Given Default) % of exposure lost if default occurs 20%–80% 30%–70%
EAD (Exposure at Default) Outstanding amount owed at default Loan balance + CCF × undrawn As drawn + derivatives
EL (Expected Loss) Average anticipated loss per year Portfolio-specific Portfolio-specific

Key distinctions: - EL is what the bank expects to lose on average — it is priced into loan rates and covered by provisions. - Unexpected Loss (UL) is the deviation from expectation — covered by regulatory capital. - Capital requirements under Basel target a 99.9% confidence interval for UL.


Basel Credit Risk Approaches: At a Glance

Feature Standardised Approach (SA) Foundation IRB (F-IRB) Advanced IRB (A-IRB)
PD External ratings / fixed weights Bank estimates Bank estimates
LGD Fixed supervisory (45% senior unsecured) Fixed supervisory Bank estimates
EAD Fixed supervisory CCFs Fixed supervisory CCFs Bank estimates
Data requirement None (uses external ratings) Min. 5 years PD history Min. 5 yrs PD, 7 yrs LGD/EAD
Regulatory approval required? No Yes (PRA/ECB/Fed) Yes (most burdensome)
Capital floor (Basel 3.1) N/A — floor reference SA output × 72.5% minimum SA output × 72.5% minimum
Typical user Smaller/simpler banks Mid-sized banks, challengers Large international banks

Capital floor: Post-Basel 3.1, IRB-calculated RWAs cannot fall below 72.5% of the equivalent SA RWA. This limits capital relief from model optimism.


Scorecard Development: Key Steps

  1. Data assembly — Identify development sample, define observation window, define default window (typically 12 months).
  2. Definition of default — Align with CRR2 Article 178 (90+ days past due; unlikely to pay).
  3. Binning and WoE transformation — Discretise continuous variables; compute WoE per bin.
  4. Information Value (IV) screening — Exclude variables with IV < 0.02; flag IV > 0.50 for data leakage review.
  5. Logistic regression — Fit on WoE-transformed features; assess statistical significance and direction.
  6. Score scaling — Convert log-odds output to integer points using base score, PDO, and target odds.
  7. Validation — Hold-out sample testing; compute Gini, AUC, KS; PSI on score distribution.
  8. Calibration — Ensure predicted PDs match observed default rates by rating grade.
  9. Documentation — Complete model development documentation per SR 11-7 standards.
  10. Independent validation — Validation by staff independent of the development team.

Model Validation Metrics: Reference Table

Discrimination Metrics (does the model rank borrowers correctly?)

Metric Formula Minimum Acceptable Good Excellent
Gini Coefficient 2 × AUC − 1 ≥ 0.30 0.45–0.60 > 0.60
AUC-ROC Area under ROC curve ≥ 0.65 0.72–0.80 > 0.80
KS Statistic Max|CDF_good − CDF_bad| ≥ 0.20 0.30–0.50 > 0.50

Note: Higher Gini/AUC/KS = better discrimination. If Gini > 0.70, check for data leakage — future information may have leaked into training.

Calibration Metrics (are predicted PDs accurate?)

Metric What it measures Acceptable
Hosmer-Lemeshow Chi-squared test of predicted vs observed by decile p-value > 0.05 (fail to reject H0)
Brier Score Mean squared error of predictions Lower is better
PD Accuracy Ratio Observed default rate / predicted PD by grade Within ±20% of PD per grade

Stability Metrics (is the population the model was built on still the population being scored?)

Metric Formula No action Monitor Model review required
PSI (Score) Σ(Ai − Ei) × ln(Ai/Ei) < 0.10 0.10–0.25 > 0.25
PSI (Input Variable) Same formula per variable < 0.10 0.10–0.25 > 0.25

PSI interpretation: When PSI > 0.25, the model is being applied to a population materially different from the one it was built on. Model outputs cannot be relied upon without an overlay or redevelopment.


SR 11-7 Model Risk Management: Key Requirements

The Federal Reserve's SR 11-7 (2011) sets out the standard for model risk governance. Key requirements practitioners must know:

SR 11-7 Requirement What it means in practice
Model definition Any quantitative method producing a decision output is a "model" — including vendor models, spreadsheet tools, and judgment-augmented models.
Conceptual soundness The model's theory, assumptions, and design must be appropriate for its intended use.
Validation independence Validators must be independent of model developers. The same individual cannot develop and validate a model.
Ongoing monitoring Model performance must be tracked continuously in production; alerts when performance deteriorates.
Outcomes analysis Predicted outcomes must be compared to actual outcomes once sufficient time has passed.
Model inventory A complete, current register of all models in use.
Model risk appetite The board approves an explicit statement of tolerable model risk.
Vendor model treatment Vendor models are not exempt — they must be validated with the same rigour as internal models.
Senior management accountability Model risk governance is a board/senior management responsibility, not solely a technical function.

TTC vs. PIT: The Key Distinctions

Characteristic Through-the-Cycle (TTC) Point-in-Time (PIT)
Definition Average PD across a full economic cycle Current PD given current macro conditions
Volatility Low — stable across economic conditions High — rises in recessions, falls in expansions
Procyclicality Low — capital requirements are stable High — provisions surge in downturns
Required for Basel IRB capital calculations IFRS 9 Expected Credit Loss (ECL)
Data requirement Long history (full cycle) Shorter, but needs macro linkage
Typical approach Agency-mapping, long-run default rates Scorecard calibrated to current conditions + macro overlay

Most large banks maintain both: a TTC core model for capital, with a macro satellite model producing PIT adjustments for IFRS 9 provisions.


IFRS 9 Three-Stage Framework

Stage Status Provision PD Used
Stage 1 Performing — no SICR since origination 12-month ECL 12-month PIT PD
Stage 2 Significant Increase in Credit Risk (SICR) Lifetime ECL Lifetime PIT PD path
Stage 3 Credit-impaired (effective default) Lifetime ECL (on net carrying amount) 100% by definition

SICR triggers (common examples): - PD has increased by ≥ 200 basis points vs origination - Internal rating downgraded by 2+ notches - 30+ days past due (rebuttable presumption) - Watchlist classification


Model Governance: Practitioner Checklist

Use this checklist when assessing a credit risk model governance framework:

Model Inventory - [ ] All models formally registered with unique ID, owner, purpose, materiality tier - [ ] Inventory updated within 30 days of any model change - [ ] Vendor models included in the inventory - [ ] Retired models documented and de-registered

Model Development - [ ] Development documentation complete before model goes into production - [ ] Training/test/validation samples clearly defined and segregated - [ ] Data sources documented; data quality assessment completed - [ ] Variable selection methodology documented with IV/statistical rationale - [ ] Model limitations explicitly stated in documentation

Model Validation (Independence) - [ ] Validator(s) independent of development team - [ ] Validation scope covers conceptual soundness, methodology, and implementation - [ ] Out-of-time or out-of-sample testing performed - [ ] Validation findings documented with severity ratings - [ ] All open findings tracked to remediation with target dates

Ongoing Monitoring - [ ] Monthly/quarterly monitoring report produced and reviewed - [ ] PSI calculated for scores and key input variables - [ ] Override rates tracked, reported, and included in monitoring - [ ] Escalation triggers and thresholds defined for each model - [ ] Annual validation (minimum) for Tier 1 models

Model Use - [ ] Override policy documented: when overrides are permitted, who approves, and how they are recorded - [ ] Model cannot be applied outside its documented scope without validation committee approval - [ ] Relevant staff trained on model limitations and appropriate use - [ ] Model outputs reviewed by human judgment for high-value decisions

Board/Senior Management - [ ] Model risk appetite approved by the board - [ ] Quarterly model risk report presented to ALCO/Risk Committee - [ ] Model risk material to ICAAP Pillar 2 assessment - [ ] Head of Model Risk (or equivalent) has direct access to CRO/board


Information Value (IV) Quick Reference

IV Value Predictive Power Action
< 0.02 Negligible Exclude from model
0.02–0.10 Weak Use with caution; investigate
0.10–0.30 Moderate Include
0.30–0.50 Strong Include
> 0.50 Suspiciously strong Check for data leakage, target leakage, or look-ahead bias

Key Regulatory References

Regulation / Guidance Issuer Key Provisions Relevant to This Chapter
SR 11-7 (2011) US Federal Reserve / OCC Model risk management framework — the global standard
CRR2 (EU 575/2013 as amended) European Parliament / Council IRB eligibility, definition of default (Art. 178), capital floors
EBA/GL/2017/16 European Banking Authority PD, LGD, EAD estimation requirements for IRB
EBA/DP/2021/04 European Banking Authority ML in credit risk — supervisory discussion paper
IFRS 9 IASB Expected Credit Loss; three-stage model; SICR
Basel III Final Standard (2017) BCBS Capital floor (72.5%), IRB scope restrictions
TRIM (ECB, 2017–2021) European Central Bank IRB model targeted review; common deficiencies

Chapter 15 of Regulatory Technology (RegTech): A Practitioner's Guide