Foundation IRB Specification¶

Basel 3.1 Foundation IRB changes: reduced senior LGD, higher PD floors, covered bond LGD, 1.06 scaling removal, and GBP-native SME correlation thresholds.

Regulatory Reference: PRA PS1/26 Art. 153–163, 178, CRE31–32 Test Group: B31-B

Requirements Status¶

Overview¶

Basel 3.1 makes significant changes to the F-IRB framework, primarily reducing the benefit of internal models by tightening supervisory parameters and removing the scaling factor.

Key Changes from CRR¶

Supervisory LGD (Art. 161)¶

Unsecured Exposures¶

Collateral-Type LGDS Values (Art. 230, CRE32.9–12)¶

When exposures are secured by eligible collateral, the F-IRB supervisory LGDS values apply:

Overcollateralisation Requirements¶

Unchanged from CRR:

Blended LGD Formula (Art. 230)¶

For partially secured exposures, the effective LGD blends secured and unsecured components:

LGD_effective = (E_unsecured / EAD) x LGDU + sum_i((E_i / EAD) x LGDS_i)

Where:

• LGDU = unsecured LGD (40% non-FSE senior, 45% FSE, 75% subordinated)
• LGDS_i = secured LGD for collateral type i
• E_unsecured = exposure amount not covered by collateral
• E_i = exposure amount secured by collateral type i

See CRM Specification for haircut application details.

PD Floors (Art. 160, 163)¶

Corporate, Sovereign, and Institution¶

Retail¶

Capital Formula (Art. 153)¶

The IRB capital formula is unchanged in structure but the 1.06 scaling factor is removed:

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

Where:

• N[.] = cumulative normal distribution function
• G(.) = inverse cumulative normal distribution (PPF)
• R = asset correlation (see below)
• MA = maturity adjustment factor
• PD = probability of default (floored)
• LGD = loss given default (supervisory or floored internal)

Asset Correlation (Art. 153(2)–(4))¶

Corporate, Sovereign, Institution:

R = 0.12 x f(PD) + 0.24 x (1 - f(PD))
where f(PD) = (1 - exp(-50 x PD)) / (1 - exp(-50))

SME Correlation Adjustment (Art. 153(4)):

SME_adj = 0.04 x (1 - (s - 4.4) / 39.6)
R_SME = R_corporate - SME_adj

Where s = clip(turnover_GBP, 4.4, 44.0) (millions GBP).

Retail Mortgage / Residential RE: Fixed R = 0.15

QRRE: Fixed R = 0.04

Retail Other:

R = 0.03 x f(PD) + 0.16 x (1 - f(PD))
where f(PD) = (1 - exp(-35 x PD)) / (1 - exp(-35))

FI Scalar (Art. 153(2))¶

For large or unregulated financial sector entities, a 1.25× multiplier is applied to the asset correlation:

R_fse = R x 1.25

Triggered by apply_fi_scalar = True in the input data. Applies to large FSEs (total assets ≥ GBP 79 billion per PS1/26 Glossary p. 78, which corresponds to CRR Art. 142(1)(4) at EUR 70bn) and all unregulated FSEs (Art. 153(2)). See Model Permissions for the distinction between the FI scalar (correlation multiplier) and Art. 147A approach restrictions (all FSEs → F-IRB only).

Effective Maturity (Art. 162)¶

PRA PS1/26 substantially rewrites Art. 162, requiring all IRB firms (F-IRB and A-IRB) to calculate effective maturity — the CRR F-IRB fixed-maturity option is deleted.

Key Changes from CRR Art. 162¶

Art. 162(2A) Calculation Methods¶

Precedence rules (Art. 162(2)):

• (g)/(h) take precedence over (b), (c), (d), (da)
• (c) takes precedence over (b)
• (k) takes precedence over (a) — revolving exposures always use facility termination date

Art. 162(3) — One-Day Maturity Floor¶

Retained from CRR unchanged: the one-day floor still requires the conjunctive trigger daily re-margining AND daily revaluation (plus documentation for prompt liquidation / set-off). It is not correct that Art. 162(3) widened to "or" under Basel 3.1 — only the 5-day / 10-day intermediate floors in Art. 162(2A)(c)/(d) switched CRR's "and" to Basel 3.1's "or" (daily re-margining or revaluation + prompt liquidation). Art. 162(3) applies to daily-margined repos / derivatives / margin lending under a master netting agreement and to qualifying short-term exposures (FX settlement, self-liquidating trade finance ≤ 1yr, securities settlement, electronic payments).

See CRR F-IRB specification for the full qualifying short-term exposure list.

Maturity Adjustment Formula¶

b = (0.11852 - 0.05478 x ln(PD))^2
MA = (1 + (M - 2.5) x b) / (1 - 1.5 x b)

Where:

• M = effective maturity, floored at 1.0 year and capped at 5.0 years
• Default maturity in code (when maturity_date null): 2.5 years
• Retail exposures: MA = 1.0 (no maturity adjustment)

Purchased Receivables (Pool Treatment & Dilution Risk)¶

PS1/26 carries forward the CRR top-down treatment for purchased receivables: a pool of receivables purchased from a third-party seller is risk-weighted as a single exposure on the basis of pool-level PD, LGD and dilution-risk parameters, rather than by rating each individual obligor. Two parallel risk components apply:

1. Default risk of the underlying obligors (treated like other corporate or retail IRB exposures, but parameterised at pool level when individual PDs are not estimable).
2. Dilution risk — the risk that the receivable amount is reduced by credits, returns, set-offs, or counter-claims unrelated to obligor default — calculated as a separate exposure with its own EAD, PD, LGD and 1-year maturity (Art. 157).

The treatment splits along corporate vs retail receivables, with two key linkages back to the F-IRB framework already specified above: senior / subordinated / dilution LGD values from Art. 161(1)(e)–(g) (40% / 100% / 100% under PS1/26) and the 0.05% corporate PD floor from Art. 160(1).

(a) Pool as a Single Exposure (Top-Down Treatment)¶

PS1/26 Art. 154(5)–(7) (retail) and the corporate analogues in Art. 160(2) / Art. 161(1)(e)–(f) treat the pool, not its individual obligors, as the unit of measurement. Eligibility of the pool is conditional on the operational requirements in Art. 184, summarised below:

If the institution has full recourse to the seller for both default risk and dilution risk, the exposure is treated as a collateralised exposure to the seller and Articles 151(2), 152 and 158(1)–(4) cease to apply at pool level (Art. 151(2), final sentence).

(b) Dilution Risk as a Separate Component¶

Art. 157 establishes that dilution risk is calculated as a distinct exposure alongside the default-risk exposure on the same pool. The two components have independent parameters:

(c) Art. 160(2) / 160(6) — Estimating PD and EL for the Dilution Component¶

When the institution cannot estimate PD for the obligors in the pool (or the estimates do not meet the Section 6 IRB requirements), Art. 160(2) provides three top-down PD methods for purchased corporate receivables:

For the dilution-risk component specifically (Art. 160(6)):

PD_dilution = EL_estimate_for_dilution_risk
LGD_dilution = 100% (Art. 161(1)(g)) under Foundation IRB

A-IRB firms operating under Art. 147A may, as an alternative, decompose the dilution EL into PD and LGD components reliably and use the decomposed PD with the matching decomposed LGD (Art. 161(2)(b)(ii)), subject to the same Art. 184 operational requirements. Unfunded credit protection on the dilution PD is recognised under Credit Risk Mitigation (CRR) Part Article 191A.

(d) Art. 154(5)–(7) — Retail Pool Eligibility Conditions¶

To qualify for the retail risk-weight function (Art. 154(1)) at pool level, the purchased receivables must satisfy the operational requirements of Art. 184 plus the four pool eligibility conditions in Art. 154(5):

Pools that meet (a)–(d) are routed through the retail F-IRB / A-IRB risk-weight function with correlation per Art. 154(1) (general retail) and the relevant retail PD floor from Art. 163(1) (0.10% mortgage / 0.10% QRRE revolver / 0.05% other).

Cross-Reference Summary¶

Key Scenarios¶

Acceptance Tests¶