Provisions Specification¶

Provision treatment, expected loss calculation, and EL vs provisions comparison.

Regulatory Reference: CRR Articles 110, 111(1)(a)-(b), 159; PRA Rulebook (CRR Firms) Art. 158

Test Group: CRR-G

Requirements Status¶

Pipeline Position¶

Provisions are resolved before CCF application in the pipeline:

resolve_provisions → CCF → initialize_ead → collateral → guarantees → finalize_ead

This ordering complies with CRR Art. 111(1)(a) (on-balance sheet: accounting value after specific CRA) and Art. 111(1)(b) (off-balance sheet: nominal after specific CRA, then × CCF). Note: Art. 111(2) governs derivative exposure values, not provisions.

Multi-Level Beneficiary Resolution¶

Provisions can be allocated at different levels and are resolved in priority order:

Direct allocations are applied first. Facility-level and counterparty-level provisions are distributed proportionally based on each exposure's share of the total ead_gross.

SA Approach (CRR Art. 110, 111(1))¶

Under the Standardised Approach, provisions use a drawn-first deduction approach:

# Step 1: Absorb provision against drawn amount first
provision_on_drawn = min(provision_allocated, max(0, drawn_amount))

# Step 2: Remainder reduces nominal before CCF (capped at nominal)
provision_on_nominal = min(provision_allocated - provision_on_drawn, nominal_amount)
nominal_after_provision = nominal_amount - provision_on_nominal

# Step 3: CCF applied to adjusted nominal
ead_from_ccf = nominal_after_provision × CCF

# Step 4: Final EAD (provisions already baked in)
EAD = (max(0, drawn) - provision_on_drawn) + interest + ead_from_ccf

The finalize_ead() step does not subtract provisions again — they are already reflected in ead_pre_crm via the drawn-first deduction.

New Columns (SA)¶

IRB Approach (Art. 158-159)¶

Under IRB, provisions are tracked (provision_allocated) but not deducted from EAD. The provision columns are set to zero:

provision_deducted = 0
provision_on_drawn = 0
provision_on_nominal = 0

Instead, the calculator computes Expected Loss for comparison:

EL = PD × LGD × EAD

Basel 3.1: Post-Model EL Adjustment (Art. 158(6A))¶

Under Basel 3.1, total EL amounts must be increased to reflect any post-model adjustments on EL required under Art. 146(3)(c). This is a B31 addition not present under CRR.

EL vs Provisions Comparison (Art. 159)¶

The comparison pool 'B' (provisions side) includes: - General credit risk adjustments (CRA) - Specific CRA for non-defaulted exposures - Additional value adjustments (AVAs per Art. 34) - Other own funds reductions

Art. 159(3) — Two-Branch Comparison Rule¶

Art. 159 partitions the EL-vs-provisions comparison into four labelled amounts:

Art. 159(3) sets out two distinct branches depending on whether the non-defaulted and defaulted pools are aligned in sign:

Branch 1 — split branch (A > B AND D > C, simultaneously):
    negative amount = B − A    (non-defaulted shortfall)
    positive amount = D − C    (defaulted excess)

Branch 2 — combined branch (all other cases):
    if (A + C) > (B + D):
        negative amount = (B + D) − (A + C)
    if (B + D) > (A + C):
        positive amount = (B + D) − (A + C)

The split branch prevents specific CRAs on defaulted exposures from offsetting expected loss amounts on other (non-defaulted) exposures.

The negative amount (shortfall) is deducted in full from CET1 under Art. 36(1)(d). The positive amount (excess) is added to T2 under Art. 62(d), subject to the cap defined below.

Art. 62(d) — T2 Cap on EL Excess¶

The Art. 159(3) positive amount (EL excess) is admissible to Tier 2 capital under Art. 62(d), but only up to a hard ceiling expressed as a percentage of IRB credit-risk RWA:

T2_credit_cap = 0.006 × IRB_credit_risk_RWA
T2_credit     = min(EL_excess, T2_credit_cap)

The 0.6% cap is calculated on the un-floored IRB credit-risk RWA, not on the post-CCB or post-output-floor TREA. CRR has no output floor, so this distinction does not arise here — under CRR the IRB RWA base for the cap is simply the IRB credit-risk RWA from Art. 153.

Worked example — both branches¶

Scenario A: combined branch with shortfall (CET1 deduction)

Inputs (£m):
  A = 100   (non-defaulted EL)
  B =  60   (non-defaulted provisions + AVAs + other reductions)
  C =  40   (defaulted EL)
  D =  30   (defaulted specific CRAs)
  IRB credit-risk RWA = 12,500

Branch test: A > B (100 > 60) AND D > C? D = 30, C = 40, so D < C.
  → Split branch does NOT apply. Use combined branch.

(A + C) − (B + D) = 140 − 90 = 50 > 0
  → Negative amount = (B + D) − (A + C) = −50.
  → CET1 deduction (Art. 36(1)(d)) = £50m.
  → No T2 credit. T2 cap not engaged.

Scenario B: combined branch with excess, cap binds (T2 credit at cap)

Inputs (£m):
  A =  60
  B = 100
  C =  20
  D =  40
  IRB credit-risk RWA = 12,500

Branch test: A > B? 60 < 100, so split branch does NOT apply.

(B + D) − (A + C) = 140 − 80 = 60 > 0
  → Positive amount (EL excess) = £60m.

T2 cap (Art. 62(d)):
  T2_credit_cap = 0.006 × £12,500m = £75m
  T2_credit     = min(£60m, £75m)  = £60m   (cap not binding)

If instead IRB RWA = £8,000m:
  T2_credit_cap = 0.006 × £8,000m  = £48m
  T2_credit     = min(£60m, £48m)  = £48m   (cap binds — £12m of excess unrecognised)

Scenario C: split branch (Art. 159(3)(a)/(b))

Inputs (£m):
  A = 100   (non-defaulted EL)
  B =  60   (non-defaulted provisions)
  C =  20   (defaulted EL)
  D =  50   (defaulted specific CRAs)
  IRB credit-risk RWA = 10,000

Branch test: A > B (100 > 60) AND D > C (50 > 20)? Yes — split branch applies.

Negative amount (a) = B − A = 60 − 100 = −40   (non-defaulted shortfall £40m)
Positive amount (b) = D − C = 50 − 20 =  30    (defaulted excess £30m)

Capital impact:
  CET1 deduction (Art. 36(1)(d)) = £40m  (full non-defaulted shortfall)
  T2 cap (Art. 62(d)) = 0.006 × £10,000m = £60m
  T2 credit          = min(£30m, £60m) = £30m  (cap not binding)

Note: The £30m defaulted excess is NOT netted against the £40m non-defaulted
shortfall. Cross-pool netting is precisely what Art. 159(3) split branch
prohibits — both the full deduction and the (capped) credit flow through.

Portfolio-Level Summary (ELPortfolioSummary)¶

The aggregator computes a portfolio-level ELPortfolioSummary with:

Slotting Approach¶

Same as IRB: provisions are tracked but not deducted from EAD.

Key Scenarios¶

Additional spec scenarios validated through the above:

• SA OBS provision deduction: Provision reduces nominal before CCF application (validated within G1 pipeline — drawn-first mechanics apply to OBS)
• Multi-level beneficiary resolution: Direct, facility, and counterparty-level provisions resolved in priority order with pro-rata distribution (validated through G1 pipeline and unit tests)
• Art. 159(3) two-branch rule: Non-defaulted shortfall and defaulted excess computed separately when conditions hold (validated through G2/G3 and dedicated unit tests)

Acceptance Tests¶