Basel III Supervision: PD, LGD, RWA, VaR and the Output Floor, with a Worked Banking Case

Finalised Basel III is no longer a forward-looking project: since 1 January 2025, most of the framework has applied to European banks through the CRR3 regulation and the CRD6 directive, published in the Official Journal on 19 June 2024. But the structure is still moving — targeted deferrals, diverging timetables across jurisdictions, and a capital floor phasing in gradually.

This article sets out what applies today, then works through a full numerical case: a mid-sized bank whose supervisory parameters we compute across the three main Pillar 1 risks — credit and counterparty, market, operational — before measuring the effect of the output floor on its CET1 ratio.

1. Where finalised Basel III stands in 2026

European Union

CRR3 has applied since 1 January 2025. CRD6 transposition into national law falls during 2026. Two major adjustments are worth noting.

First, the Fundamental Review of the Trading Book (FRTB) has been deferred. The Commission adopted a delegated act postponing the application of market risk requirements by one further year, to 1 January 2027. Through 2026, European banks therefore continue to compute their market risk requirement under the previous regime.

Second, the Union exercised its national discretion on operational risk by setting the Internal Loss Multiplier (ILM) to 1 for all institutions. The Pillar 1 requirement therefore depends solely on the business indicator. Loss history does not disappear: it moves to Pillar 2 and feeds the SREP. Institutions with a business indicator of EUR 750 million or more must still compute and disclose their annual operational losses.

United Kingdom and United States

The PRA published its final policy (PS1/26) on 20 January 2026. The UK Basel 3.1 rules take effect on 1 January 2027, with the internal model approach for market risk itself deferred to January 2028.

In the United States, the trajectory has changed in nature. On 19 March 2026, the federal agencies issued a revised proposal formally rescinding the 2023 framework, with a stated orientation towards capital neutrality. The comment period closed on 18 June 2026.

For an international banking group, the practical consequence is a durable misalignment: the same portfolio can produce three different capital requirements depending on the subsidiary’s jurisdiction, on timetables two to three years apart. This is currently one of the main difficulties in consolidated prudential steering.

2. The case: Banque Continentale

A mid-sized European institution, approved for the advanced internal ratings-based approach on its corporate portfolio. Business indicator of EUR 3.2 billion, CET1 capital of EUR 2,400 million, total internal-model RWA of EUR 18,500 million, and standardised-approach RWA of EUR 26,000 million.

The figures that follow are illustrative but fully reproducible: every formula is spelled out and every total has been verified.

3. Credit and counterparty risk

3.1 The four parameters

  • PD — one-year probability of default, estimated internally under IRB, now constrained by a CRR3 input floor of 0.05% for corporate and retail exposures (0.1% for qualifying revolving exposures).
  • LGD — loss given default. CRR3 lowers the regulatory value for senior unsecured exposures to non-financial corporates to 40%, against 45% retained for bank and financial counterparties.
  • EAD — exposure at default. For derivatives it is built up through the standardised approach for counterparty credit risk (SA-CCR).
  • M — effective maturity, capped at 5 years and floored at 1 year.

3.2 The regulatory formula

The capital requirement K for a corporate exposure rests on three building blocks. Asset correlation declines with PD, between 24% and 12%:

R = 0.12 × (1 − e−50·PD)(1 − e−50)+ 0.24 × [ 1 − (1 − e−50·PD)(1 − e−50) ]
b = ( 0.11852 − 0.05478 · ln PD )2
MA = 1 + (M − 2.5) · b1 − 1.5 · b
K = [ LGD · Φ(Φ−1(PD) + R · Φ−1(0.999)1 − R)− PD · LGD ] · MA
RWA = K × 12.5 × EAD
Φ is the standard normal cumulative distribution function and Φ−1 its inverse. R is asset correlation, b the maturity adjustment factor, M effective maturity in years.

The 12.5 factor is the reciprocal of 8%: it converts a capital requirement into a risk-weighted asset. Subtracting PD × LGD removes expected loss, which provisioning covers rather than capital — what regulatory capital covers is unexpected loss at a one-year horizon and a 99.9% quantile.

3.3 Applied to the portfolio

ExposurePDLGDMRMAKRWEADRWA
Senior unsecured corporate0.80%40%2.50.20041.28210.0603875.48%100.075.48
Investment-grade corporate (floored PD)0.05%40%2.50.23701.75180.0139717.47%50.08.73
Bank counterparty (derivatives)0.15%45%2.50.23131.51060.0299437.42%23.88.91
Total credit and counterparty RWA93.12

Amounts in EUR million.

The second line deserves comment. The bank estimated an internal PD of 0.03% for this counterparty. The CRR3 floor lifts it to 0.05%, taking the risk weight from roughly 13% to 17.47% — close to a third more RWA on that exposure alone. This is the regulator’s intent: to bound internal-model variability at the high-quality end of the spectrum, where dispersion between institutions was widest.

Note too the counter-intuitive behaviour of the maturity adjustment: the lower the PD, the higher b and the larger MA. On the investment-grade exposure MA reaches 1.75 against 1.28 on the riskiest one. Rating migration risk weighs proportionally more on high-quality names.

3.4 Derivative exposure: SA-CCR

The EUR 23.8 million EAD used above cannot be read off a balance sheet: it is constructed. The standardised approach for counterparty credit risk combines current replacement cost and potential future exposure, scaled by an alpha factor of 1.4:

EAD = 1.4 × ( RC + PFE )
     = 1.4 × ( 5 + 12 )
     = EUR 23.8 million
RC: current replacement cost, net of collateral, floored at zero. PFE: potential future exposure. The 1.4 coefficient is the prudential alpha factor.

Replacement cost is market value net of collateral received, floored at zero. Potential future exposure aggregates asset-class add-ons computed on adjusted notionals, scaled by supervisory deltas and maturity factors, then modulated by a multiplier recognising over-collateralisation. The 1.4 factor is a flat prudential coefficient inherited from internal-model calibration.

4. Market risk: from VaR to expected shortfall

The substantive change FRTB brings fits in one sentence: 99% 10-day VaR gives way to 97.5% expected shortfall. The difference is conceptual rather than arithmetic.

VaR answers “what loss will not be exceeded in 99% of cases?”. It says nothing about the remaining 1%. Expected shortfall answers “what is the average loss across the worst 2.5% of scenarios?”. It therefore incorporates the shape of the tail, and it has the sub-additivity property VaR lacks — the measure of an aggregate portfolio cannot exceed the sum of the measures of its components.

4.1 Why 97.5%

The threshold was not picked at random. Under a Gaussian assumption, 97.5% ES and 99% VaR give near-identical results: the 99% quantile is 2.326 standard deviations, 97.5% ES is 2.338. The Basel Committee calibrated the switch to be neutral on a normal distribution.

Apply it to Banque Continentale’s trading portfolio, whose 10-day volatility comes out at EUR 1.8 million.

Distributional assumption99% VaR97.5% ESDifference
Normal4.1874.208+0.5%
Student-t, 5 degrees of freedom4.6924.910+4.7%

Amounts in EUR million, identical variance in both cases.

The point of the reform lies in the second row. At identical variance, simply moving to a fat-tailed distribution — closer to actual market returns — widens the gap between the two measures. ES captures that thickening; VaR ignores it by construction. On a portfolio loaded with options or credit exposures, the gap becomes substantial.

4.2 What else FRTB adds

Reducing FRTB to the ES-for-VaR substitution would be misleading. Three further changes weigh at least as heavily on the final requirement.

  • Differentiated liquidity horizons, from 10 to 120 days depending on the risk-factor class, replace the single 10-day horizon.
  • The risk factor eligibility test excludes insufficiently observable factors from the internal model; these then attract a dedicated capital charge.
  • The boundary between banking book and trading book becomes rigid, with binding reclassification rules — a direct answer to the regulatory arbitrage seen before 2008.

On top of this sits a fully redesigned standardised approach, combining a sensitivities-based method, a default risk charge and a residual risk add-on. It now serves as both floor and fallback, which makes it structurally relevant even for internal-model banks.

5. Operational risk: the standardised approach

Finalised Basel III abolishes every earlier approach — basic indicator, standardised, advanced measurement — in favour of a single method. The principle is simple: regulatory capital follows business size, optionally adjusted for loss history.

Capital = BIC × ILM
BIC = ∑buckets ( business indicator × marginal coefficient )
ILM = ln( e − 1 + LCBIC0.8 )
LC = 15 × average annual losses over 10 years
BIC: business indicator component. ILM: internal loss multiplier, set to 1 in the European Union. LC: loss component.

The business indicator aggregates three components: interest, leases and dividends; services; and financial operations. Marginal coefficients are progressive by tranche.

BucketBusiness indicatorMarginal coefficient
1≤ EUR 1bn12%
2EUR 1bn to 30bn15%
3> EUR 30bn18%

For Banque Continentale, with a business indicator of EUR 3.2 billion:

BIC = 12% × EUR 1.0bn + 15% × EUR 2.2bn
     = 0.12 + 0.33 = EUR 0.450bn = EUR 450 million

With average operational losses of EUR 25 million a year over ten years, the loss component stands at EUR 375 million, giving an LC/BIC ratio of 0.833 and an ILM of 0.949. Under the full Basel standard the bank would therefore carry operational capital of EUR 427 million.

RegimeILMCapitalEquivalent RWA
Full Basel standard0.949427.05,337
European Union (CRR3)1.000450.05,625

Amounts in EUR million.

The result is surprising at first: by neutralising the ILM, the European Union raises this bank’s requirement by EUR 288 million of RWA. The reason is that its loss history is better than the average implicit in the calibration — an ILM below 1 would have benefited it. The trade-off is deliberate: the Union prioritised simplicity and comparability, accepting that they penalise well-run institutions at Pillar 1, and restoring risk sensitivity at Pillar 2 through the SREP.

6. The output floor: the real tipping point

This is the most structurally significant measure in finalised Basel III. The principle: RWA computed under internal models cannot fall below 72.5% of what they would be under the standardised approach. The aim is to bound the dispersion in risk weights across institutions for comparable risks.

Phase-in is gradual: 50% in 2025, then annual steps to 72.5% in 2030, with transitional treatments for certain exposure classes — residential mortgages, unrated corporates — running to end-2032.

YearFactorFloorRWA appliedBinding constraintCET1 ratio
202550.0%13,00018,500Internal models12.97%
202655.0%14,30018,500Internal models12.97%
202760.0%15,60018,500Internal models12.97%
202865.0%16,90018,500Internal models12.97%
202970.0%18,20018,500Internal models12.97%
203072.5%18,85018,850Output floor12.73%

RWA in EUR million, based on EUR 26,000m standardised RWA, EUR 18,500m internal-model RWA and EUR 2,400m CET1.

This table repays close reading. For five years the floor does not bite: the bank is steered by its internal models and sees nothing coming. Then, at the final step, the constraint flips all at once — EUR 350 million of additional RWA, 24 basis points of CET1 ratio, with no management decision taken and not one euro of new risk booked.

This is exactly where the steering challenge sits. A bank that discovers the floor effect in 2029 has no room left to manoeuvre. One that modelled it today has several levers: redirecting origination towards segments where the gap between standardised and internal-model treatment is narrowest, improving the quality of collateral recognised under the standardised approach, or stepping back from IRB on portfolios where it no longer delivers a saving once the floor applies.

System-wide, the EBA estimates the increase in minimum Tier 1 requirements at around 7.8% once fully phased in, and around 8.6% for the largest banks.

7. Parameter summary

RiskKey parametersMeasureStatus in 2026 (EU)
CreditPD, LGD, EAD, M, R, MARWA = K × 12.5 × EADApplicable, input floors in force
CounterpartyRC, PFE, alpha = 1.4EAD = 1.4 × (RC + PFE)Applicable
Market99% VaR → 97.5% ES, liquidity horizonsES + DRC + RRAODeferred to 1 January 2027
OperationalBI, BIC, ILMCapital = BIC × ILMApplicable, ILM = 1 in the EU
Cross-cuttingOutput floorRWA ≥ 72.5% of standardised RWAPhasing in to 2030

Conclusion

Finalised Basel III is not merely a tightening of requirements. Its underlying logic is a rebalancing between risk sensitivity and cross-institution comparability: internal models survive, but bounded by input floors on the parameters and by a global floor on the output.

Three workstreams follow for finance and risk functions. The first is dual instrumentation: producing standardised and internal-model RWA in parallel across the whole portfolio, which presupposes a standard-approach data quality long left neglected. The second is multi-year projection of the floor, the only way to spot the tipping year before it arrives. The third is managing jurisdictional divergence, for groups consolidating subsidiaries on timetables several years apart.

The figures presented here are those of a textbook case. The method is transferable: every formula is the one in the regulatory text, and every result can be recomputed.

References

  • Regulation (EU) 2024/1623 (CRR3) and Directive (EU) 2024/1619 (CRD6), OJEU, 19 June 2024
  • European Commission, delegated act deferring the application of market risk requirements to 1 January 2027
  • Basel Committee, Basel III: Finalising post-crisis reforms, December 2017
  • Basel Committee, Minimum capital requirements for market risk (FRTB), January 2019
  • Bank of England, PRA, PS1/26 — Implementation of Basel 3.1: Final rules, 20 January 2026
  • US federal banking agencies, revised capital proposal, 19 March 2026
  • EBA, Basel III monitoring exercise

This article presents a methodological analysis for educational purposes. It does not constitute regulatory advice, legal advice, or an investment recommendation. The calibrations used are illustrative and must be adapted to each institution’s profile and validated with its supervisor.


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