Defaulted Exposures Specification¶

Basel 3.1 treatment of defaulted exposures under the Standardised Approach and IRB, including the provision-coverage risk weight split and RESI RE exception.

Regulatory Reference: PRA PS1/26 Art. 127, Art. 153(1)(ii), Art. 154(1)(i), CRE20.88 Test Group: B31-K

Requirements Status¶

ID	Requirement	Priority	Status
FR-10.1	SA defaulted: provision-coverage 100%/150% RW split	P0	Done
FR-10.2	SA defaulted: provision threshold at 20% of outstanding amount	P0	Done
FR-10.3	SA defaulted: unsecured portion determined by the CRM method (Art. 127(2))	P0	Done
FR-10.4	SA defaulted: RESI RE non-income-dependent flat 100% exception	P0	Done
FR-10.5	IRB F-IRB defaulted: K = 0 (Art. 153(1)(ii))	P0	Done
FR-10.6	IRB A-IRB defaulted: K = max(0, LGD − BEEL) (Art. 154(1)(i))	P0	Done
FR-10.7	IRB defaulted: no 1.06 scaling factor under Basel 3.1	P0	Done

Overview¶

Basel 3.1 introduces a more granular SA treatment of defaulted exposures compared to CRR. Under CRR, defaulted exposures generally received a flat 100% or 150% risk weight with limited distinction. Basel 3.1 introduces a provision-coverage mechanism that rewards firms for adequate provisioning.

Default Trigger — Art. 178

This specification covers the consequence of default (risk weight treatment). The definition of default — the Art. 178 two-limb trigger (unlikeliness-to-pay and 90 DPD), UTP indicators, materiality thresholds, suspension rules, and cure/probation requirements — is documented in the shared Default Definition (Art. 178) specification. The calculator consumes default status via the upstream is_defaulted flag and routes accordingly.

Key Changes from CRR¶

Feature	CRR	Basel 3.1	Reference
SA risk weight mechanism	Flat 100%/150%	Provision-coverage split	Art. 127
Provision threshold denominator	Pre-provision unsecured exposure value	Outstanding amount of the item or facility (gross)	Art. 127(1)
RESI RE non-income exception	None	Flat 100% regardless of provisions	Art. 127(3) (was cited as 127(1A) in earlier drafts; PDF numbers as para 3)
IRB F-IRB defaulted	K = 0; RW includes 1.06	K = 0; no 1.06 (Art. 153(3) left blank)	Art. 153(1)(ii)
IRB A-IRB defaulted	K = max(0, LGD − BEEL); 1.06 in RW	K = max(0, LGD − BEEL); no 1.06	Art. 154(1)(i)

SA Defaulted Exposures (Art. 127)¶

Provision-Coverage Mechanism¶

For SA defaulted exposures, the risk weight for the unsecured portion depends on the level of specific provisions relative to the outstanding amount of the item or facility:

provision_ratio = specific_provisions / outstanding_amount

Provision Ratio	Risk Weight	Reference
≥ 20%	100%	Art. 127(1)(b)
< 20%	150%	Art. 127(1)(a)

Where:

specific_provisions = specific credit risk adjustments per Art. 110 and Commission Delegated Regulation (EU) No 183/2014
outstanding_amount = the outstanding amount of the item or facility (gross, before CRM adjustments)

Denominator Differs from CRR

CRR Art. 127(1) uses: "the unsecured part of the exposure value if those specific credit risk adjustments and deductions were not applied" — the pre-provision unsecured exposure value.

PRA PS1/26 Art. 127(1) uses: "the outstanding amount of the item or facility" — the gross outstanding amount (the full facility, not limited to the unsecured portion, and not net of provisions).

The PRA denominator is typically larger, making it easier to reach the 20% threshold for a given level of provisioning.

Secured Portion Treatment¶

PS1/26 Art. 127(2) defers to the CRM method the institution applies (Art. 191A(2)) to determine the unsecured portion:

Financial Collateral Comprehensive Method (FCCM — default for SA): eligible financial collateral has already reduced ead_final in the CRM stage. The value entering the defaulted override IS the unsecured value, and Art. 127(1) applies to it flat.
Financial Collateral Simple Method (FCSM): handled downstream by apply_fcsm_rw_substitution, which blends the defaulted RW with the collateral RW per the substitution rule.
Real estate: eligible RE collateral routes through class reclassification (mortgage treatment) upstream; it does not reappear as a secured portion inside the defaulted override.

The defaulted override therefore does NOT re-apply a secondary secured/unsecured split on non-financial collateral columns — that would double-count the CRM reduction and, for low-RW classes like retail (75%), drag the defaulted RW below the 100% floor required by Art. 127(1)(b).

RWA_defaulted = ead_final × provision_based_rw

RESI RE Non-Income-Dependent Exception¶

Art. 127(3) / CRE20.88

Defaulted exposures secured by residential real estate that are not dependent on cash flows generated by the property (i.e., standard owner-occupied mortgages) receive a flat 100% risk weight regardless of the provision ratio.

This exception recognises that residential mortgages with recourse to the borrower's income have a different risk profile from income-dependent real estate exposures.

if exposure.is_residential_re and not exposure.is_income_dependent:
    rw = 100%  # Flat, regardless of provision ratio

Scope of Exception

The exception applies only to residential RE exposures that meet the Art. 124A qualifying criteria and are not income-dependent. Income-producing residential RE, buy-to-let, and commercial RE defaulted exposures all follow the standard provision-coverage mechanism.

IRB Defaulted Exposures¶

F-IRB Defaulted (Art. 153(1)(ii))¶

For F-IRB defaulted exposures, the capital requirement formula component K is set to zero:

K = 0

The risk weight for F-IRB defaulted is therefore driven entirely by the expected loss (EL) component:

RW = max(0, 12.5 x (LGD - BEEL))

Where:

LGD = supervisory LGD (40% senior non-FSE, 45% FSE, 75% subordinated)
BEEL = best estimate of expected loss — the firm's estimate of loss given default has occurred

1.06 Scaling Factor Removed

Under CRR, the IRB capital formula included a 1.06 scaling factor (Art. 153(3)). Basel 3.1 removes this — Art. 153(3) is "[Provision left blank]" in PRA PS1/26. This applies to all IRB exposures, not just defaulted.

A-IRB Defaulted (Art. 154(1)(i))¶

For A-IRB defaulted exposures, K uses the firm's own LGD estimate:

K = max(0, LGD - BEEL)

Where:

LGD = the firm's internal LGD estimate for the defaulted exposure, subject to LGD floors
BEEL = best estimate of expected loss

The risk weight is:

RW = max(0, 12.5 x K)

Expected Loss for Defaulted¶

Art. 158(5) sets a different EL rule for the two IRB approaches:

Approach	Defaulted EL amount	Rationale
F-IRB defaulted	`EL = PD x LGD x EAD = 1 x LGD x EAD`	Standard Art. 158(5) first formula with PD = 1
A-IRB defaulted	`EL = BEEL x EAD`	Art. 158(5) closing proviso — firm's own best estimate substitutes for the PD x LGD product

PRA PS1/26 Art. 158(5) verbatim (ps126app1.pdf p. 107)

"An institution using the Foundation IRB Approach or Advanced IRB Approach shall, subject to the specific treatment laid down in paragraphs 6 and 6A, calculate the expected loss (EL) and expected loss amounts for exposures to corporates and institutions and for retail exposures in accordance with the following formulae:

Expected loss (EL) = PD · LGD

Expected loss amount = EL · exposure value

except for defaulted exposures (PD = 1) where the institution uses the Advanced IRB Approach, EL shall be BEEL."

The substitution applies only to the A-IRB EL amount (the figure that feeds Pool C of the Art. 159 provisions comparison). The RW formulas in Art. 153(1)(b) and Art. 154(1)(i) reference BEEL for both F-IRB and A-IRB defaulted exposures — that is a capital-calculation mechanic distinct from the Art. 158(5) EL-amount definition.

BEEL — Best Estimate of Expected Loss (Art. 158(5), Art. 181(1)(h)(ii))¶

Definition. BEEL is the institution's own estimate of the economic loss expected on a defaulted exposure over the period from the default event to the final liquidation or recovery, expressed as a fraction of exposure at default. It is the A-IRB counterpart to the supervisory LGD applied to non-defaulted exposures.

PRA Rulebook source. BEEL is a defined term in the Credit Risk: Internal Ratings Based Approach (CRR) Part of the PRA Rulebook (Rule 1.3): "BEEL means an institution's best estimate of expected loss for a defaulted exposure as referred to in point (h)(ii) of Article 181(1)". Art. 181(1)(h)(ii) sets the estimation standards an institution must satisfy before it may recognise its own BEEL estimate:

Downturn conditions. BEEL must be estimated on the basis of economic conditions observed during periods of stress relevant to the exposure, consistent with the downturn-LGD requirements of Art. 181(1)(b).
Evidence of unexpected additional loss during recovery. Where the institution has evidence of unexpected loss during the recovery period, the BEEL estimate must be greater than or equal to the expected economic loss given default (i.e. BEEL ≥ LGD-in-default after recoveries).
No cherry-picking. Observed recovery realisations must be used symmetrically — favourable and unfavourable outcomes must both inform the estimate.
Governance and independence. Estimates must be subject to the same validation, human oversight, and back-testing processes applied to other A-IRB parameters (Art. 185 validation rules apply by reference).

Scope — A-IRB only. BEEL is an A-IRB-specific input for the EL-amount calculation in Art. 158(5); under F-IRB the EL amount uses the standard Art. 158(5) formula PD x LGD x EAD with PD = 1, so F-IRB firms do not need to estimate BEEL separately for Pool C. The supervisory LGD parameter (40% senior non-FSE, 45% FSE, etc.) already provides the conservative loss expectation under F-IRB.

Sovereign/central-bank carve-out. Under PS1/26 Art. 147A(1)(a), sovereign, central-bank, RGLA, PSE, MDB and international-organisation exposures are excluded from A-IRB; BEEL therefore cannot arise for these classes — any exposure to a defaulted quasi-sovereign counterparty must be treated under SA (Art. 127).

Required input. The engine consumes BEEL as a row-level input named beel of type Float64. The column is defined in src/rwa_calc/data/schemas.py on loans, contingents, and facility_details, defaults to 0.0, and is read by engine/irb/adjustments.py solely when is_defaulted = True and the exposure is routed through the A-IRB approach (see Default Definition spec — BEEL Companion Input).

beel > 0 is not a default trigger — DQ008 surfaces the contradiction

PS1/26 Art. 181(1)(h)(ii) and Art. 158(5) define BEEL only for defaulted exposures, so it would be tempting to treat beel > 0 as sufficient evidence of default. The engine deliberately does not do that — firms whose A-IRB model pipelines emit a BEEL-style value alongside lgd for every advanced-IRB customer (not just defaulted ones) would otherwise see those rows silently mass-flagged as defaulted. The classifier's _build_is_defaulted_expr (engine/stages/classify/attributes.py) derives is_defaulted from two explicit signals only — cp_default_status and the row-level is_defaulted flag — and a non-zero beel on any non-defaulted row surfaces as a single aggregate DQ008 warning carrying the total count of offending exposures (ERROR_BEEL_ON_NON_DEFAULTED_EXPOSURE in contracts/errors.py, severity WARNING, category DATA_QUALITY), mirroring the CLS006 / CLS008 roll-up pattern. The calc is unaffected on those rows — beel is only consumed when the derived is_defaulted is True. To eliminate the warning, restrict beel population to defaulted rows in the upstream loader.

Relationship to LGD-in-default. The A-IRB capital formula K = max(0, LGD − BEEL) uses the institution's LGD-in-default estimate (the firm's current best view of post-default economic loss, used in the RW structure) minus BEEL (the firm's best estimate of EL amount already accrued). Where BEEL ≥ LGD-in-default, K = 0 and the RW collapses to max(0, 12.5 × 0) = 0; Pool C of the Art. 159 comparison still carries the full BEEL × EAD amount as the defaulted EL contribution.

CRR → PS1/26 terminology change

Pre-revocation CRR used the symbol ELBE (Expected Loss Best Estimate) in Art. 158(5) and Art. 181(1)(h). PS1/26 renames this to BEEL (Best Estimate of Expected Loss) with no substantive change in the estimation standards — Art. 181(1)(h)(ii) wording tracks the CRR version. The engine's beel column and internal variable names use the PS1/26 term. Legacy CRR documentation and model validation reports that reference ELBE denote the same parameter.

Interaction with Art. 158(6A) post-model EL uplift

PS1/26 introduces a new paragraph 6A requiring institutions to increase the total EL amounts (paragraphs 5 and 6) to reflect any post-model adjustments recognised under Art. 146(3)(c). For A-IRB defaulted exposures this means the BEEL × EAD contribution is uplifted by any PMA component before entering Pool C of the Art. 159 comparison. See Provisions spec — Art. 158(6A) EL Monotonicity. No equivalent paragraph existed under pre-revocation CRR.

Key Scenarios¶

Scenario ID	Description	Expected Outcome
B31-K1	SA defaulted, provisions ≥ 20% of outstanding amount	100% RW
B31-K2	SA defaulted, provisions < 20% of outstanding amount	150% RW
B31-K3	SA defaulted, zero provisions	150% RW on full ead_final
B31-K4	SA defaulted, RESI RE non-income-dependent	100% RW (flat, Art. 127(3))
B31-K5	SA defaulted, RESI RE non-income with collateral columns populated	100% RW (flat, Art. 127(3) overrides)
B31-K6	SA defaulted, RESI RE income-dependent (IPRRE)	Provision-coverage test on full ead_final
B31-K7	SA defaulted corporate, non-fin collateral columns populated	Full provision-based RW (columns ignored by defaulted override)
B31-K8	SA defaulted, B31 vs CRR denominator difference	100% under B31, 150% under CRR
B31-K9	F-IRB defaulted corporate	K=0, RW=0, EL = LGD × EAD
B31-K10	A-IRB retail defaulted	K = max(0, LGD − BEEL)
B31-K11	A-IRB corporate defaulted (no 1.06 scaling under B31)	RWA matches CRR (no 1.06 in Art. 153(1)(ii))
B31-K12	A-IRB corporate defaulted, BEEL > LGD	K=0 (floored)

Acceptance Tests¶

Group	Scenarios	Tests	Pass Rate
B31-K: Defaulted Exposures	K1–K12	31	100% (31/31)