Basel 3.1 Framework Differences¶

Key differences from CRR including output floor, PD/LGD floors, and removal of supporting factors.

Regulatory Reference: PRA PS1/26

Overview¶

Basel 3.1 (effective 1 January 2027 in the UK) introduces significant changes to the credit risk framework. The calculator supports both regimes via a configuration toggle.

Key Differences¶

Differentiated PD Floors (Basel 3.1)¶

PRA PS1/26 Art. 160(1) (corporate, sovereign, institution) and Art. 163(1) (retail):

A-IRB LGD Floors (Basel 3.1)¶

Corporate / Institution (Art. 161(5)):

Retail (Art. 164(4)):

LGD_floor = (E_u / E) x 30% + sum_i (E_s_i / E) x LGDS_i

*Values reflect PRA PS1/26 implementation. BCBS standard values differ (Receivables: 15%, CRE: 10%, RRE: 10%, Other Physical: 20%).

F-IRB Supervisory LGD (Art. 161)¶

Art. 161 LGD Values¶

Art. 230 LGDS Values (Secured Portions)¶

Output Floor¶

The output floor ensures IRB RWA cannot fall below a percentage of what the SA would produce:

RWA_final = max(RWA_IRB, floor_percentage x RWA_SA)

Transitional Schedule (PRA PS1/26 Art. 92 para 5)¶

The PRA compressed the BCBS 6-year phase-in to a 4-year schedule:

Note: Art. 92 para 5 says institutions "may apply" these transitional rates — they are permissive. Firms can voluntarily use 72.5% from day one.

Output Floor Adjustment (OF-ADJ)¶

The full output floor formula from PRA PS1/26 Art. 92(2A) is:

TREA = max{U-TREA; x × S-TREA + OF-ADJ}

Where:

• U-TREA = un-floored total risk exposure amount (Art. 92(3))
• S-TREA = standardised total risk exposure amount (Art. 92(3A)) — calculated without IRB, SFT VaR, SEC-IRBA, IAA, IMM, or IMA
• x = floor percentage (see transitional schedule above)
• OF-ADJ = 12.5 × (IRB_T2 – IRB_CET1 – GCRA + SA_T2)

The OF-ADJ reconciles the different treatment of provisions under IRB and SA:

Under IRB, EL shortfall adds to capital requirements (CET1 deduction) while excess provisions provide T2 relief. Under SA, general credit risk adjustments provide T2 relief directly. The 12.5 multiplier converts own-funds amounts to risk-weighted equivalents. Without this adjustment, the floor comparison would not be on a like-for-like basis.

For COREP template mapping of OF-ADJ components, see the output reporting spec.

Entity-Type Carve-Outs (Art. 92(2A)(b)–(d))¶

The output floor does not apply universally. Art. 92(2A) specifies which entity/basis combinations must use the floored TREA formula; all others use U-TREA directly:

Floor applies (Art. 92(2A)(a)):

• Standalone UK institution — individual basis
• Ring-fenced body in sub-consolidation group — sub-consolidated basis
• CRR consolidation entity (not international subsidiary) — consolidated basis

Exempt — use U-TREA only (Art. 92(2A)(b)–(d)):

• (b) Non-ring-fenced institution — sub-consolidated basis
• (c) Ring-fenced body in sub-consolidation group; non-standalone UK institution — individual basis
• (d) CRR consolidation entity that is an international subsidiary — consolidated basis

Supervisory Haircut Comparison¶

CRR Haircuts (3 maturity bands)¶

Basel 3.1 Haircuts (5 maturity bands)¶

PRA PS1/26 Art. 224 Table 3 (10-day holding period):

Currency mismatch haircut remains 8% under both frameworks (CRR Art. 224 / CRE22.54).

Volatility Scaling (Art. 226)¶

Supervisory haircuts from Art. 224 assume daily revaluation and a 10-day holding period. Two scaling adjustments may apply:

Art. 226(2) — Liquidation Period Scaling¶

Scales haircuts between holding periods (e.g., 10-day table value to 5-day repo period):

H_m = H_n × sqrt(T_m / T_n)

Implementation: scale_haircut_for_liquidation_period() in engine/crm/haircut_tables.py (the pack-binding shim that homes the relocated haircut table builders); applied via the liquidation_period_days column in engine/crm/haircuts.py.

Art. 226(1) — Non-Daily Revaluation Adjustment¶

When collateral is revalued less frequently than daily, an additional scaling applies on top of the liquidation period adjustment:

H = H_m × sqrt((N_R + T_m − 1) / T_m)

Example: Government bond CQS 1 (0-1y), weekly revaluation (N_R = 5), repo (T_m = 5):

• Table haircut (10-day): 0.5%
• After Art. 226(2): 0.5% × sqrt(5/10) = 0.354%
• After Art. 226(1): 0.354% × sqrt((5 + 5 - 1)/5) = 0.354% × 1.342 = 0.475%

CRR vs Basel 3.1 Structural Change¶

CRR Art. 226 was a single (unnumbered) article covering non-daily revaluation only. The liquidation period scaling formula was in Art. 225(2)(c) (own-estimates approach). PRA PS1/26 removes Art. 225 entirely (own-estimates approach no longer permitted) and restructures Art. 226 into two numbered paragraphs: (1) non-daily revaluation, (2) liquidation period scaling. The formulas themselves are unchanged.

See CRR CRM spec and B31 CRM spec for full regulatory text.

SA Residential Real Estate Risk Weights (Basel 3.1)¶

Basel 3.1 replaces CRR Art. 125 (flat 35% up to 80% LTV) with two distinct residential RE treatments:

General (not income-dependent) — Art. 124F: Loan-Splitting

• Secured portion (up to 55% of property value) → 20% RW
• Residual portion → counterparty RW (75% for individuals per Art. 124L)

Income-producing (cash-flow dependent) — Art. 124G, Table 6B: Whole-Loan

SA Commercial Real Estate Risk Weights (Basel 3.1)¶

Basel 3.1 replaces CRR Art. 126 (proportion-based split: 50% on portion up to 50% MV, counterparty RW on excess — applied uniformly to all CRE) with entity-type-differentiated treatment under Art. 124H:

Exposures failing Art. 124A qualifying criteria fall to Art. 124J: 150% (income-dependent), counterparty RW (residential non-income-dependent), or max(60%, counterparty RW) (commercial non-income-dependent).

Slotting Risk Weights (Basel 3.1)¶

PRA PS1/26 Art. 153(5) Table A defines two slotting weight tables — non-HVCRE and HVCRE:

Non-HVCRE (OF, CF, PF, IPRE)¶

HVCRE¶

Slotting Subgrades (Table A Columns A/B/C/D)¶

PRA PS1/26 Art. 153(5) Table A splits Strong into columns A and B, and Good into columns C and D:

Column B/D is the default assignment (Art. 153(5)(c)). Column A/C may be used when:

• < 2.5yr remaining maturity (Art. 153(5)(d)) — optional for all SL types
• IPRE Strong meets all four sub-conditions of Art. 153(5)(e): (i) substantially stronger underwriting, (ii) very low LTV, (iii) investment-grade income stream including tenant income ≥ 100% of the obligor's debt service obligations, and (iv) no ADC characteristics
• PF Strong meets Art. 153(5)(f) — substantially stronger underwriting and characteristics; no additional quantitative sub-conditions

For non-HVCRE types, the values are identical to CRR — PRA restructured the format from maturity-split tables to A/B/C/D columns but preserved all risk weight values. The HVCRE row is a PRA PS1/26 introduction (UK CRR has no HVCRE table). See Key Differences for the full comparison and Slotting Approach spec for implementation details.

Financial Institution Correlation Multiplier (Art. 153(2))¶

The 1.25x correlation multiplier applies to exposures to financial institutions only (not non-financial corporates):

• Large financial sector entities (LFSEs) — regulated FSEs meeting a total-assets threshold that is framework-specific (see table below).
• Unregulated financial sector entities — regardless of size.

This multiplier is already implemented via the requires_fi_scalar flag in the classifier and _polars_correlation_expr() in the IRB formulas. It applies under both CRR and Basel 3.1 frameworks.

Note: There is no separate "large corporate" correlation multiplier for non-financial corporates in either the BCBS standard or PRA PS1/26. See key-differences.md § Financial Sector Correlation Multiplier for the parallel CRR/B31 comparison and the distinction from the Art. 147A(1)(e) GBP 440m revenue approach restriction.

Credit Conversion Factors (Art. 111 Table A1)¶

PRA PS1/26 replaces CRR Annex I with a 7-row Table A1. Key changes: CRR maturity-based commitment split (50%/>1yr, 20%/≤1yr) replaced by flat 40% "other commitments" bucket; UCC from 0% to 10%; F-IRB CCFs aligned to SA (Art. 166C). UK residential mortgage commitments carved out at 50% (Row 4(b)) — a PRA-specific addition preventing the maturity-removal from reducing capital for irrevocable mortgage offers (BCBS would assign 40%). See CCF specification for full Table A1.

A-IRB CCF Floor (CRE32.27)¶

A-IRB own-estimate CCFs must be at least 50% of the SA CCF for the same item type.

Post-Model Adjustments (Art. 146(3), 153(5A), 154(4A), 158(6A))¶

Basel 3.1 introduces mandatory post-model adjustments (PMAs) — conservative overlays on A-IRB model outputs with no CRR equivalent. PMAs address material model non-compliance without requiring full model re-estimation.

Components¶

The mortgage RW floor default is 10% for UK residential mortgage exposures (PRA supervisory parameter). The general scalars are set per model via PostModelAdjustmentConfig.

Sequencing (Mandatory)¶

Art. 154(4A) prescribes a strict ordering:

1. Step 1 — Mortgage floor (Art. 154(4A)(b)): Floor the modelled risk weight
2. Step 2 — PMA scalar (Art. 154(4A)(a)): Scale the floor-adjusted RWEA

The PMA scalar amplifies the post-floor RWEA, not the raw model output. Reversing the order would produce incorrect results because the scalar would inflate a sub-floor RW before the floor is applied.

EL Monotonicity (Art. 158(6A))¶

EL_adjusted >= EL_unadjusted

PMAs cannot decrease expected loss. The pma_el_scalar must be ≥ 0, ensuring conservative RWA overlays do not inadvertently reduce EL shortfall calculations (Art. 159).

Defaulted EL — BEEL Substitution (Art. 158(5))¶

BEEL (Best Estimate of Expected Loss) is the A-IRB firm's own estimate of post-default economic loss, estimated under the Art. 181(1)(h)(ii) standards. The substitution applies only to the A-IRB Pool C EL amount in the Art. 159 comparison; the A-IRB capital formula K = max(0, LGD − BEEL) (Art. 154(1)(i)) uses BEEL in the RW structure separately. Pre-revocation CRR used the symbol ELBE; PS1/26 renames to BEEL with no substantive change. Sovereigns and other Art. 147A(1)(a) quasi-sovereign classes are excluded from A-IRB, so BEEL never arises for them.

See the Defaulted Exposures spec — BEEL for estimation standards and required inputs.

Output Floor Interaction¶

PMAs are included in the un-floored TREA (U-TREA) used for the output floor comparison. They cannot be avoided by flooring to SA — the floor applies to the post-PMA total.

See the A-IRB specification for the complete implementation detail and COREP column mapping.

IRB Effective Maturity (Art. 162)¶

PRA PS1/26 substantially rewrites Art. 162. The most significant structural change is the deletion of F-IRB fixed supervisory maturities — all IRB firms must now calculate M.

The revolving maturity change (Art. 162(2A)(k)) typically increases M for revolving facilities, leading to higher maturity adjustments and therefore higher capital. The deletion of the F-IRB 0.5-year repo maturity means repo exposures will use the full cash-flow or contractual calculation, generally increasing M from 0.5 to ≥ 1 year.

See the CRR F-IRB specification and Basel 3.1 F-IRB specification for full regulatory text and implementation details.

Configuration¶

Switch between frameworks using the configuration factory:

from rwa_calc.contracts.config import CalculationConfig

# CRR (current)
config = CalculationConfig.crr(reporting_date=date(2026, 12, 31))

# Basel 3.1
config = CalculationConfig.basel_3_1(reporting_date=date(2027, 1, 1))