What are the key data and modeling requirements for estimating PD, LGD, and EAD under the Advanced IRB approach?

Question

AcadiFi · Accepted Answer

Under A-IRB, banks must estimate **PD, LGD, and EAD** using internal models that meet rigorous regulatory standards. Each parameter has specific data requirements, calibration rules, and common pitfalls.

**Probability of Default (PD)**

| Requirement | Detail |
|---|---|
| Minimum data | 5 years of default observations (7 preferred) |
| Calibration | Long-run average default rate, not point-in-time |
| Floor | 0.03% for corporate/sovereign exposures |
| Methodology | Rating migration models, scorecards, structural models |

**Key Pitfalls:**
- Using too-short data window that misses a full credit cycle
- Confusing point-in-time PD (current condition) with through-the-cycle PD (long-run average)
- Low-default portfolios (sovereign, bank, large corporate) where observed defaults are rare

**Loss Given Default (LGD)**

| Requirement | Detail |
|---|---|
| Minimum data | 7 years of recovery data |
| Calibration | Must reflect **downturn conditions** (not average cycle) |
| Floor | None prescribed globally, but some jurisdictions set floors |
| Components | Recovery rate, time to recovery, workout costs, discount rate |

```mermaid
flowchart TD
    A["Default Event"] --> B["Collect recoveries over workout period"]
    B --> C["Cash recoveries: collateral sales, guarantees, debt restructuring"]
    B --> D["Workout costs: legal, administrative, opportunity cost"]
    C --> E["Gross Recovery Rate"]
    D --> E
    E --> F["Discount to present value at appropriate rate"]
    F --> G["LGD = 1 - Discounted Recovery Rate"]
    G --> H["Apply downturn adjustment"]
```

**Downturn LGD Worked Example:**

Fairview Bank's commercial real estate portfolio shows:
- Average-cycle LGD: 28% (based on property recoveries)
- During 2008-2010 downturn: LGD was 47% (property values fell 35%)
- Downturn LGD estimate for capital: **47%**

**Exposure at Default (EAD)**

| Requirement | Detail |
|---|---|
| Minimum data | 5 years of drawdown observations |
| Key concept | Credit Conversion Factor (CCF): how much of undrawn commitments get drawn before default |
| Formula | EAD = Drawn Amount + CCF x Undrawn Commitment |
| Calibration | Should reflect pre-default drawdown behavior |

**CCF Example:**

Mercer Bank's revolving credit facilities (historical analysis of 200 defaults):
- Average drawn at observation: 55% of limit
- Average drawn at default: 78% of limit
- **CCF = (78% - 55%) / (100% - 55%) = 51%**

For a $20M facility with $11M currently drawn:
- EAD = $11M + 0.51 x ($20M - $11M) = $11M + $4.59M = **$15.59M**

**Model Validation Requirements:**
- Annual backtesting of PD (predicted vs. actual default rates)
- Benchmarking against external data (rating agencies, peer banks)
- Stress testing of parameters under adverse scenarios
- Independent model validation team review

For more on A-IRB modeling, explore our FRM Part II course.

What are the key data and modeling requirements for estimating PD, LGD, and EAD under the Advanced IRB approach?

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