Advanced IRB Specification¶

Advanced IRB calculation with internal LGD and CCF estimates.

Regulatory Reference: CRR Articles 153-154, 158(5), 178

Test Group: CRR-C

Requirements Status¶

Overview¶

A-IRB uses the same capital requirement formula and correlation functions as F-IRB, but the bank provides its own estimates for LGD and (optionally) maturity and CCF, rather than using supervisory values.

Key Differences from F-IRB¶

LGD Floors¶

CRR Portfolio-Level LGD Floors (Art. 164(4))¶

CRR Art. 164(4) (as amended by CRR2, Regulation 2019/876) imposes portfolio-level LGD floors for retail exposures secured by immovable property:

These are not per-exposure input floors — they require that the exposure-weighted average LGD across the entire retail property portfolio does not fall below the threshold. Exposures benefiting from central government guarantees are excluded from the calculation.

Art. 164(5)–(8) grant the PRA power to set higher minimum LGD values based on periodic assessment of loss experience data, forward-looking market developments, and financial stability concerns.

Basel 3.1 Per-Exposure LGD Floors¶

Under Basel 3.1, the following per-exposure input floors apply:

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

Art. 161(5) has two limbs. Point (a) sets a flat 25% floor for unsecured exposures and for exposures where the firm chooses not to take recognised funded credit protection into account. Point (b) covers secured and partially secured exposures where the firm does take the protection into account: the floor is the Art. 230 (single collateral type) / Art. 231 (multiple types) LGD* value, computed with 25% substituted for LGDU (Art. 161(5)(b)(iii)) and the following LGDS values (Art. 161(5)(b)(iv)):

A partially secured exposure is therefore floored on the blend, not on the flat 25% and not on the bare collateral-type LGDS. For a GBP 10m corporate loan with GBP 4m of recognised financial collateral the floor is 0.6 x 25% + 0.4 x 0% = 15%.

The weights are shares of the Art. 230(1) exposure basis E' = E x (1 + HE), where E is ead_for_crm — the CCF=100% exposure value (Art. 223(4)) — and HE is the exposure's own volatility haircut (Art. 223(5), non-zero only on securities-lending rows). It is not the post-CCF ead_gross: for a GBP 1m undrawn committed facility at a 40% CCF with GBP 200k of recognised cash, the floor is 25% x 800k/1m = 20%, not the 25% x 200k/400k = 12.5% a post-CCF divisor gives. Every LGDS lies below every LGDU, so the smaller divisor over-weights the secured share and understates the floor.

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

Retail "Other Secured" LGD Floor — Art. 164(4)(c)¶

For retail exposures secured by collateral other than RRE, the LGD floor is a blended value combining the secured collateral floor (LGDS) and the unsecured floor (LGDU = 30%), weighted by the secured and unsecured portions of the exposure — the same structure as the Foundation Collateral Method in Art. 230.

The LGDS values by collateral type are:

Where no split between secured/unsecured portions is available, the conservative approach is to apply the relevant collateral-type LGDS directly (or LGDU=30% if unsecured).

Implementation: src/rwa_calc/engine/irb/formulas.py — _lgd_floor_blended_expression() computes the weighted-average floor using the crm_alloc_* columns from the Art. 231 sequential waterfall. The formula: LGD_floor = (E_unsecured / E') × LGDU + Σ_i (E_i / E') × LGDS_i, with E' = ead_for_crm × (1 + HE) shared with the LGD itself via engine/crm/expressions.py::lgd_star_exposure_basis_expr(). The same expression serves both limbs — Art. 161(5)(b) for corporates and institutions and Art. 164(4)(c) for retail — because the LGDS tables are identical and only LGDU differs: 50% retail_qrre, 30% retail_other, 25%* every other class. It applies to every exposure class except retail_mortgage (flat 5% per Art. 164(4)(a)) once recognised collateral is present, and returns null — deferring to the flat / single-type floor — when nothing is recognised or the allocation columns are absent.

FI Scalar¶

The 1.25x correlation multiplier for large/unregulated financial sector entities applies equally to A-IRB and F-IRB (Art. 153(2), CRE31.5). The LFSE (large financial sector entity) total-assets threshold is EUR 70 billion under CRR Art. 142(1)(4) and GBP 79 billion under Basel 3.1 (PS1/26 Glossary p. 78, with Note "corresponds to Article 142(1)(4) of CRR"). The 1.25 factor is applied to the asset correlation coefficient R, which has a non-linear effect on the capital requirement K.

Calculation¶

The capital requirement formula, correlation functions, maturity adjustment, and RWA computation are identical to F-IRB. See F-IRB Specification for full details.

Post-Model Adjustments (Basel 3.1)¶

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

Basel 3.1 introduces a minimum risk weight floor for UK residential property exposures under IRB:

• Regulatory floor: 10% per Art. 154(4A)(b) for non-defaulted IRB residential mortgage exposures
• Scope: All non-defaulted IRB exposures secured by residential immovable property
• Formula: floor_adjustment = max(0, floor_rw - modelled_rw) × EAD
• RWEA: RWEA_adjusted = RWEA_modelled + floor_adjustment
• Reported: COREP column 0253 (adjustment for mortgage RW floor)
• Configurable: Via PostModelAdjustmentConfig.mortgage_rw_floor (default should be 10%)

General Post-Model Adjustments (Art. 146(3) / Art. 158(6A))¶

Art. 146(3) establishes the root obligation: firms using IRB must apply post-model adjustments to compensate for known model deficiencies. Art. 158(6A) specifies the EL monotonicity constraint. Firms must apply PMAs to both RWEA and EL:

• PMA on RWEA: RWEA_adjusted = RWEA_modelled × (1 + pma_rwa_scalar)
• PMA on EL: EL_adjusted = EL_modelled × (1 + pma_el_scalar)
• Reported: COREP column 0252 (adjustment for post-model adjustments)

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

Art. 154(4A) prescribes the following sequential order for RWEA adjustments:

1. Mortgage RW floor — Art. 154(4A)(b): applied first to establish the post-floor RWEA base
2. General PMA scalars and unrecognised-exposure adjustments — Art. 154(4A)(a): applied to the post-floor RWEA from step 1

Double Default Removal (Basel 3.1)¶

CRR Art. 153(3) provided a double-default treatment for guaranteed exposures. Under PRA PS1/26, Art. 153(3) is "[Note: Provision left blank]" — the double-default treatment has been removed. Any exposures that previously benefited from double-default must fall back to standard parameter substitution (Art. 236) or risk weight substitution (Art. 235).

A-IRB CCF Restrictions (Basel 3.1)¶

Under Basel 3.1, own CCF estimates are only permitted for revolving facilities (Art. 166D). All non-revolving off-balance sheet items must use SA CCFs from Table A1. See CCF Specification for full details including the 50% floor on A-IRB CCF estimates.

Key Scenarios¶

Additional spec scenarios validated through the above and B31-C group:

• Internal CCF: Own-estimate CCF used for revolving facilities (validated within C1/C2 pipeline)
• FI scalar (1.25x): Correlation uplift for large/unregulated FSEs (validated through B31-B7 and pipeline tests)
• A-IRB vs F-IRB comparison: Same exposure with supervisory vs own LGD (validated through comparison test group M3.1)

Acceptance Tests¶