Probability of default
PD is the chance that a borrower defaults within one year. In the IRB approach it is a long-run average through the cycle, not the current point-in-time estimate used for pricing. That distinction matters: a through-the-cycle PD is smoother and does not spike in a recession.
PD enters the formula on a log scale. Moving from 0.5% to 1% raises the risk weight of a corporate exposure from about 62% to about 82% under CRR3, with LGD at 40%. Doubling PD roughly doubles the capital cost at low levels.
Loss given default
LGD is the share of the exposure lost if default happens, after recoveries and collateral. A 40% LGD means 40 units are lost per 100 of exposure.
Typical supervisory values: senior unsecured corporate lending sits around 45%, subordinated lending higher, exposures secured by immovable property much lower after the collateral haircut and time-to-recovery assumptions. Under CRR3 the calculator applies input floors for some retail classes, which prevent LGD from being set unrealistically low.
Exposure at default
EAD is the amount outstanding at the moment of default, including the expected drawdown of committed lines. For term loans it is close to the drawn balance; for revolving facilities and trade finance it is higher than the drawn balance because borrowers draw before they fail.
EAD does not change the risk weight. It only scales RWA and capital.
Maturity
Effective maturity, M, applies to corporate, institution and sovereign exposures in the IRB approach. It is floored at one year and capped at five, and defaults to 2.5 years when not modelled. Longer maturity raises the risk weight because there is more time for a borrower to migrate downwards.
Retail exposures carry no maturity adjustment. Their capital formula assumes a one-year horizon.
Typical ranges
| Input | Corporate | Retail mortgage |
|---|---|---|
| PD | 0.03% to 20% | 0.1% to 10% |
| LGD | 25% to 45% | 10% to 25% |
| Maturity adjustment | yes, 1 to 5 years | none |
How they combine
The IRB formula first computes a capital requirement per unit of exposure, K, from PD and LGD, then applies the maturity adjustment for corporates, then converts K into a risk weight by multiplying by 12.5.
K = LGD × Φ[(Φ⁻¹(PD) + √R × Φ⁻¹(0.999)) / √(1 − R)] − PD × LGD
The formula is written out in full, with a worked example and a PD table, on the formula page.
Common mistakes
- Entering PD or LGD as a decimal where the calculator expects a percentage.
- Using a point-in-time PD for a through-the-cycle calculation, or the reverse.
- Reporting LGD before collateral and recovery costs.
- Forgetting the drawdown on revolving facilities.
- Applying a maturity adjustment to retail exposures.
Questions
What is a normal LGD for corporate lending?
Senior unsecured corporate exposures commonly sit near 45% under supervisory values, with higher figures for subordinated debt and lower ones where collateral is strong.
Why is PD floored?
A floor prevents a model from assigning a near-zero probability to a large pool of borrowers, which would understate tail losses.
Does maturity apply to retail?
No. Retail exposures use a one-year horizon and carry no maturity adjustment.