Advanced IRB Specification¶

Basel 3.1 Advanced IRB changes: LGD floors, post-model adjustments (PMA), CCF floor at 50% of SA, double default removal, and EL monotonicity.

Regulatory Reference: PRA PS1/26 Art. 153–154, 158(5), 161(5), 164(4), 166D, 178, CRE31–32 Test Group: B31-C

Requirements Status¶

Overview¶

Basel 3.1 constrains A-IRB flexibility by introducing LGD floors that prevent internal estimates from falling below supervisory minimums, and post-model adjustments (PMA) that allow PRA to impose conservative overlays. The double default treatment is removed, replaced by parameter substitution for IRB guarantors (see CRM Specification). For funded credit protection (collateral), A-IRB firms may use LGD modelling under Art. 169A/169B or fall back to the Foundation Collateral Method (FCM, Art. 230) — see CRM Specification § LGD Modelling Collateral Method.

Key Differences from F-IRB¶

LGD Floors (Basel 3.1 Only)¶

Corporate A-IRB LGD Floors (Art. 161(5))¶

A-IRB firms must ensure their internal LGD estimates do not fall below these floors:

For partially secured exposures, the blended LGD floor is:

LGD_floor = (E_unsecured / EAD) x LGDU_floor + sum_i((E_i / EAD) x LGDS_floor_i)

Retail A-IRB LGD Floors (Art. 164(4))¶

Post-Model Adjustments (Art. 146(3), 154(4A), 158(6A))¶

PMA is a Basel 3.1 mechanism allowing the PRA to impose conservative overlays on A-IRB model outputs without requiring full model re-estimation.

Mortgage Risk Weight Floor (Art. 154(4A)(b))¶

A minimum risk weight is applied to residential mortgage exposures before general PMA:

RW_floored = max(RW_modelled, mortgage_rw_floor)

The mortgage RW floor is set by the PRA as a supervisory parameter. Default: 10%.

General PMA Scalar (Art. 146(3) / Art. 158(6A))¶

After the mortgage floor, PMA scalars are applied to both RWA and EL:

RWEA_adjusted = RWEA_modelled x (1 + pma_rwa_scalar)
EL_adjusted = EL_modelled x (1 + pma_el_scalar)

Where pma_rwa_scalar and pma_el_scalar are set per model via configuration.

Adjustment Sequencing (Art. 153(5A) / Art. 154(4A))¶

The order of adjustments is mandatory:

1. First: Apply mortgage risk weight floor (Art. 154(4A)(b))
2. Then: Apply PMA RWA/EL scalar (Art. 154(4A)(a))

EL Monotonicity (Art. 158(6A))¶

PMA application must satisfy:

EL_adjusted >= EL_unadjusted

EL must never decrease as a result of post-model adjustments. This prevents conservative RWA overlays from inadvertently reducing expected loss estimates, which would distort the EL shortfall/excess comparison (Art. 159).

A-IRB CCF Restrictions (Art. 166D)¶

Under Basel 3.1, A-IRB own-estimate CCFs are restricted to revolving facilities only (Art. 166D(1)(a)). All other off-balance sheet items must use SA CCFs from Table A1 (Art. 166D(1)(b)).

Revolving Facility Eligibility (Art. 166D(1)(a))¶

Own-estimate CCFs are permitted only where both conditions are met:

1. The facility is a revolving loan commitment — set is_revolving = True in input data
2. The facility's SA CCF (per Art. 111 Table A1) is less than 100%

Non-revolving A-IRB facilities (term loans, non-revolving commitments, guarantees, etc.) must use SA CCFs from Table A1 regardless of the firm's A-IRB permission. The is_revolving flag in the input data controls this routing in the calculator.

CCF Floor (Art. 166D(5)(a) / CRE32.27)¶

For eligible revolving facilities, the own-estimate CCF is subject to a floor:

CCF_applied = max(CCF_modelled, 0.50 × CCF_SA)

The A-IRB CCF must be at least 50% of the corresponding SA CCF (Art. 166D(5)(a)).

Expected Drawdown Incorporation (Art. 166D(2))¶

Where both an on-balance sheet item and a revolving loan commitment relate to the same facility, the firm's own CCF estimate must incorporate any expected increase in the on-balance sheet value at the point of default. This means the CCF applied to the undrawn portion should already account for the likelihood that the drawn balance will increase before default — the CCF is not applied to a static snapshot of the current undrawn amount.

Full-Facility EAD Approach (Art. 166D(3)/(4))¶

As an alternative to the standard CCF approach (drawn + undrawn × CCF), A-IRB firms may estimate a single facility-level EAD that combines both on-balance sheet and off-balance sheet components into one figure. This "full-facility EAD" replaces the separate drawn/undrawn decomposition.

The approach has two variants depending on the facility's drawdown state:

Partially or Fully Undrawn Facilities (Art. 166D(3))¶

For revolving facilities that are partially drawn or fully undrawn, the firm assigns a single EAD estimate to the entire facility. This replaces both:

• The exposure value of any related on-balance sheet item (Art. 166A(2))
• The exposure value of the revolving loan commitment (Art. 166D(1))

The single EAD must be the firm's own estimate provided in accordance with Section 6 (model validation requirements).

Fully Drawn Facilities (Art. 166D(4))¶

For revolving facilities that are currently fully drawn (no undrawn commitment remains), the firm assigns an own EAD estimate that replaces the on-balance sheet accounting value. This recognises that a revolving facility's exposure can exceed its current drawn balance — the borrower may repay and redraw, and the facility limit itself may fluctuate.

Input Field: ead_modelled¶

To use the full-facility approach, provide the ead_modelled field (type: Float64, nullable) on the facility or contingent input record:

• When present (non-null): The calculator uses this as the facility-level EAD, subject to the floors below
• When absent or null: The calculator falls back to the standard CCF-based EAD calculation (drawn + undrawn × CCF)

The field is propagated through the pipeline via FACILITY_SCHEMA → RAW_EXPOSURE_SCHEMA → RESOLVED_HIERARCHY_SCHEMA → CLASSIFIED_EXPOSURE_SCHEMA. For drawn loans without a facility commitment, ead_modelled is set to null (full-facility EAD is not applicable).

EAD Floors (Art. 166D(5))¶

Art. 166D(5) specifies three separate floor tests ensuring A-IRB EAD estimates do not fall below prudent minimums. Each floor maps to a specific EAD approach:

Floor (a): CCF Floor¶

See CCF Floor above. The modelled CCF must be at least 50% of the SA CCF for the same commitment type.

Floor (b): Facility-Level EAD Floor (Art. 166D(5)(b))¶

When using the full-facility approach for partially or fully undrawn facilities (Art. 166D(3)), the modelled EAD must not be lower than:

EAD_floor_b = EAD_on_BS + 50% × EAD_off_BS_FIRB

Where:

• EAD_on_BS = exposure value of the on-balance sheet item calculated per Art. 166A(2), disregarding Art. 166D (i.e., the drawn balance as it would be calculated without the full-facility approach)
• EAD_off_BS_FIRB = exposure value of the off-balance sheet item under the Foundation IRB Approach per Art. 166C(1) (i.e., undrawn nominal × SA CCF, since F-IRB CCFs are aligned to SA under Basel 3.1)

The 50% factor on the off-balance sheet component mirrors the 50%-of-SA-CCF floor in floor (a) — both enforce a minimum credit conversion of half the SA rate.

Implementation:

floor_b = on_balance_sheet_ead + nominal_after_provision × sa_ccf × 0.5
ead_pre_crm = max(ead_modelled, floor_b)

Floor (c): Fully-Drawn EAD Floor (Art. 166D(5)(c))¶

When using the full-facility approach for fully drawn facilities (Art. 166D(4)), the modelled EAD must not be lower than the on-balance sheet exposure value:

EAD_floor_c = EAD_on_BS

Where EAD_on_BS is calculated per Art. 166A(2), disregarding Art. 166D. This prevents the modelled EAD from falling below what the firm currently has on its balance sheet — the model may estimate higher EAD (reflecting potential redraw risk), but never lower.

Implementation:

ead_pre_crm = max(ead_modelled, on_balance_sheet_ead)

Unrecognised Exposure Adjustment (Art. 166D(6))¶

A-IRB firms must assess EADs arising from facilities or relationships that were not captured in exposure values prior to drawdown — for example, where a credit exposure materialises from a facility not originally intended to create credit risk. Where such amounts are material, the firm must quantify an unrecognised exposure adjustment reflecting the additional RWA required. This adjustment is allocated to exposure classes on a best-efforts basis.

See also the CCF specification for context on how the A-IRB CCF regime fits within the broader CCF framework.

Double Default Removal¶

Under CRR, the double default treatment (Art. 153(3) / Art. 202–203) allowed firms to recognise the joint probability of both obligor and guarantor defaulting:

K_dd = K_obligor x (0.15 + 160 x PD_guarantor)  [CRR only]

Basel 3.1 removes double default entirely — Art. 153(3) is "[Provision left blank]" in PRA PS1/26. For guaranteed exposures under IRB, firms must use parameter substitution instead — see CRM Specification.

Capital Formula¶

The A-IRB capital formula is identical to F-IRB (see F-IRB Specification):

K = LGD x N[(1-R)^(-0.5) x G(PD) + (R/(1-R))^(0.5) x G(0.999)] - PD x LGD
RW = K x 12.5 x MA

The differences are:

• LGD = firm's own estimate, subject to LGD floors (above) and CRM adjustments (Art. 169A/169B or FCM)
• PD = firm's own estimate, subject to the same PD floors as F-IRB
• MA = 1.0 for retail (no maturity adjustment); internal estimate for non-retail
• Scaling factor = 1.0 (removed under Basel 3.1)
• FI scalar = 1.25× correlation for large/unregulated FSEs (retained)

Key Scenarios¶

Acceptance Tests¶