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