The IRB approach · RiskAtoms Academy

By the end you will be able to

1Tell foundation from advanced IRB by who supplies each input, and name the IRB asset classes.
2Explain what approval requires: the minimum requirements, the use test, roll-out and permanent partial use, and the Basel 3.1 limits on who may model what.
3Apply the input floors on PD, LGD, EAD and maturity, and see when they bind.

Why it matters

RiskAtoms Bank plc weighs its corporates with its own PDs on foundation IRB: £8,934.7m of RWA, against £13,412.2m on the SA. Why not go further and use its own LGDs and conversion factors too? For 8 of its 12 corporate slices it could. Run the numbers and A-IRB comes to £8,454.3m against £5,919.8m on F-IRB. More modelling, more work, and more capital. This lesson explains the choice.

Core explanation

Who estimates what, and who may

Two approaches, three inputs

Under the IRB approach the bank's models supply the inputs and the Basel formula of L4.2.05: The IRB risk-weight formula turns them into a risk weight. The inputs are those of L3.3.06: Probability of default to L3.3.09: Exposure at default: PD, LGD, EAD and, for corporates, effective maturity M. How many the bank may estimate depends on the approach (CRE30.33):

Input	Foundation IRB	Advanced IRB	Retail IRB
PD	Own, floored at 0.05%	Own, floored at 0.05%	Own, floored at 0.05% (0.1% QRRE revolvers)
LGD	Supervisory: 40% senior, 45% to financials, 75% subordinated	Own downturn estimate, floored (25% unsecured)	Own, floored (5% mortgages)
EAD	SA conversion factors	Own CCFs on revolving lines only, floored	Own, floored
Maturity	2.5 years	Measured, between 1 and 5 years	Not used

Retail has no foundation approach: a bank using IRB for retail estimates all three inputs (CRE30.42). The IRB asset classes are corporate (with specialised lending as a sub-class), sovereign, bank and retail (CRE30.4). Specialised lending can also use slotting instead of PD estimates (CRE30.38).

Approval

A bank needs its supervisor's permission, and it must meet the minimum requirements of CRE36 on day one and after. Among them:

at least seven borrower grades for performing loans and one for default (CRE36.19);
a credit risk control unit independent of the people who originate loans (CRE36.57);
the use test: ratings and estimates play an essential role in credit approval, risk management, internal capital allocation and governance (CRE36.60);
a rating system broadly in line with the requirements for at least three years before approval (CRE36.61);
at least five years of data for PD (CRE36.79) and seven for corporate LGD (CRE36.87), five for retail LGD (CRE36.88).

The use test is the heart of it. A model built only to produce capital numbers has every reason to produce low ones. A model the bank also lends by has to be right, because the bank loses money if it is not.

A bank that adopts IRB for part of an asset class is expected to extend it across all its holdings in that asset class (CRE30.45). It may do so in phases under a roll-out plan agreed with its supervisor, and the plan may not be driven by a wish to cut capital (CRE30.47–30.48). Exposures that are immaterial in size and risk can stay on the SA for good, with approval: permanent partial use (CRE30.49). A bank on IRB may not return to the SA by choice (CRE30.50).

Would a supervisor accept this? Guess, then open.

The Basel 3.1 limits

In 2017 the Basel Committee found a “worrying degree of variability” in banks' calculation of risk-weighted assets and set out to reduce “excessive variability of risk-weighted assets” by constraining the use of internal models (BCBS high-level summary, December 2017). Three limits followed:

No A-IRB for large corporates, those in groups with revenue above €500m, averaged over three years (CRE30.34(1), CRE30.35). F-IRB is allowed.
No A-IRB for banks, other financial institutions and securities firms (CRE30.34(2)). F-IRB is allowed.
No IRB at all for equity: it goes to the SA, at the weights of L4.2.03: Off-balance sheet items and other exposures (CRE30.34, CRE30.43).

These portfolios have few defaults to estimate LGD and EAD from. Large companies and banks rarely fail, so two banks can model the same borrower very differently. Then come the input floors on what can still be modelled (CRE32):

Input	Floor (corporates)	Rule
PD	0.05%	CRE32.4 (not sovereigns)
LGD, unsecured	25%	CRE32.16
LGD, secured part	0% financial, 10% receivables, 10% real estate, 15% other physical	CRE32.16–32.17
EAD	drawn + 50% × SA CCF × undrawn	CRE32.36
Maturity	1 to 5 years	CRE32.46

Retail has its own floors: PD 0.05% (0.1% for revolving QRRE), mortgage LGD 5%, QRRE LGD 50% (CRE32.58). L3.3.06: Probability of default and L3.3.08: Loss given default and recovery met the PD and LGD floors; this table puts them together.

Sort itHow far may the bank model?

Under Basel 3.1, which approach is the most the bank could use? Revenue converts at €1.15 per pound.

Thornvale Engineering, revenue £420m
Sallowmere Logistics, revenue £640m
A senior loan to another UK bank
A loan to an insurance company
Listed shares held in the banking book
A residential mortgage

Why the bank sits where it does

Four corporate slices are large corporates, so F-IRB is the most they can have:

Borrower	Revenue (£m)	Revenue (€m)	F-IRB RWA
Bramwick Stores plc	1,100	1,265	1,650.1
Ostreth Energie GmbH	2,400	2,760	623.7
Cindral Pharma Inc	3,100	3,565	281.4
Sallowmere Logistics GmbH	640	736	459.7
Large corporates			3,014.9

The other 8 could move to A-IRB. m4-2 estimates what that would give, with the bank's own downturn LGDs, its own CCFs and measured maturities:

Borrower	Own LGD	LGD floor	M	EAD	A-IRB RWA	F-IRB RWA
Thornvale Engineering Ltd	39.0%	21.8%	5	1,431.1	966.8	560.7
Pellcourt Properties Ltd	18.9%	11.5%	4	3,034.8	1,111.6	1,043.2
Larkhollow Freight Ltd	43.1%	21.5%	3	774.8	928.7	652.3
Mirefield Care Homes Ltd	27.3%	15.1%	5	1,150.1	894.9	625.0
Quorrel Systems BV	53.0%	25.0%	4	1,034.5	1,116.7	576.1
Hastemoor Construction Ltd	63.0%	25.0%	2	644.3	1,254.5	778.1
Vellacourt Hôtels SAS	29.7%	14.5%	5	1,000.1	992.6	679.4
Graybeck Plastics Ltd	83.0%	25.0%	3	310.4	1,188.6	1,005.0
A-IRB-eligible					8,454.3	5,919.8

No floor binds: the bank's downturn LGDs are above the floors, and its own CCFs are above the EAD floor. But they are also above the supervisory values for unsecured lending, and its loans run longer than 2.5 years. So A-IRB would add £2,534.5m of RWA. Add the seven years of LGD data it would need, and F-IRB is the sensible choice. Pellcourt is the closest call: secured on let property, its own LGD of 18.9% is below F-IRB's 22.0%, but its 4-year maturity still puts A-IRB at £1,111.6m against £1,043.2m.

The mortgages are on retail IRB because retail has no foundation approach. Their RWA are £3,526.3m against £8,949.6m on the SA, and the lowest-LTV segment's LGD of 5% sits on the 5% floor (L4.2.06: IRB for retail and specialised lending). Banks, sovereigns and the consumer book stay on the SA. A supervisor would ask why the consumer book is not on IRB: is it on a roll-out plan, or immaterial? m4-2's estimate gives retail IRB there more RWA than the SA (L4.2.06: IRB for retail and specialised lending), so the bank would have to show that the saving is not the reason (CRE30.48).

The formal version

Every A-IRB input floor is a max (M-A11: Min, max, floors and caps); maturity is a clamp, a max and a min together. For a corporate exposure with drawn amount D and undrawn amount U:

\begin{aligned} \text{PD}_{\text{used}} &= \max(\text{PD}_{\text{own}},\ 0.05\%) \quad(\text{CRE32.4}) \\[4pt] \text{LGD}_{\text{used}} &= \max\Big(\text{LGD}_{\text{own}},\ 25\% \times \tfrac{E_U}{E} + \text{LGD}_S^{*} \times \tfrac{E_S}{E}\Big) \quad(\text{CRE32.16–32.17}) \\[4pt] \text{EAD}_{\text{used}} &= \max\big(D + \text{CCF}_{\text{own}} \times U,\ D + 50\% \times \text{CCF}_{\text{SA}} \times U\big) \quad(\text{CRE32.36}) \\[4pt] M_{\text{used}} &= \min\big(5,\ \max(1,\ M)\big) \quad(\text{CRE32.46}) \end{aligned}

Try it

Start with the very safe-looking loan: every floor binds. Then load Pellcourt without its downturn add-on, where only the LGD floor bites, and Quorrel, where the bank's own estimates sit well above the floors and above F-IRB.

Try itOwn estimates against the input floors

Drawn 1,138.0, undrawn 586.2 (£m). Move the bank's own estimates:

Own PD0.28%

Own downturn LGD39.0%

Own CCF on the undrawn line50%

Remaining maturity (years)5.00

Share of the exposure secured32%

Collateral on the secured part

Input	Own estimate	A-IRB uses	F-IRB uses
PDFloor: 0.05% (CRE32.4)	0.28%	0.28%	0.28%
LGDFloor: 21.8% blended (CRE32.16–32.17)	39.0%	39.0%	35.0%
EAD (£m)Floor: 1,255.3 (CRE32.36)	1,431.1	1,431.1	1,372.5
Maturity (years)Floor: 1 to 5 (CRE32.46)	5.00	5.00	2.5
RWA (£m)	966.8	966.8	560.7

A-IRB risk weight67.6%

F-IRB risk weight40.9%

RWA the floors add0.0

A-IRB less F-IRB406.1

No floor binds: the bank's own estimates go into the formula as they are. Here A-IRB gives more RWA than F-IRB: own estimates are not always lower.

F-IRB uses the supervisory LGD after collateral, the 40% SA CCF and 2.5 years. The PD floor applies to both.

Worked example

One loan, two approaches

Quorrel Systems, a Dutch technology firm with £380m of revenue. £ millions.

Quorrel on F-IRB and A-IRB

Step 1 of 7

1
Eligible?
$380 \times 1.15 = 437 \le 500 \ \Rightarrow\ \text{A-IRB allowed}$

Illustrative dataRiskAtoms Bank plc's capital book

The same made-up UK bank as Level 3: £67bn of assets and £4bn of equity at 31 December 2025, in £ millions. Module 4.1 adds its regulatory layer: own funds, deductions, risk-weighted assets by risk type, buffers, the leverage exposure and MREL, computed from the Level 3 credit, trading, derivatives and operational risk books. Every figure is illustrative, not any bank's data.

Pro forma. The book applies Basel 3.1, the 2017 finalisation of Basel III, to the 31 December 2025 balance sheet. On that date the bank still reported under the old UK CRR. The UK applies Basel 3.1 from 1 January 2027, and the internal model approach for market risk from 1 January 2028 (PRA PS1/26, paras 1.23 and 1.24). So the book shows the bank as it would look under the new rules.

Credit RWA in Module 4.2. Corporates on foundation IRB £8,934.7m (standardised £13,412.2m), mortgages on retail IRB £3,526.3m (standardised £8,949.6m), and the portfolios that stay on the standardised approach £5,277.0m. With everything standardised, credit RWA would be £27,638.9m: the credit part of the standardised total that the output floor works from.

Regulatory lens

Status as at 3 November 2026 as at 3 Nov 2026.

In the UK

From 1 January 2027 the PRA limits financial sector entities and large corporates, those with revenue above £440m, to F-IRB (Credit Risk: IRB (CRR) Part; Article 147(4C) defines the subclass). On this book the £440m line picks out the same borrowers as Basel's €500m, which is about £435m. The PRA also takes central governments and central banks off IRB (PS9/24, para 1.24), and moves income-producing real estate from F-IRB and A-IRB to the SA or, on application, slotting (PS1/26, para 2.10). Pellcourt and Vellacourt would therefore leave F-IRB. Its Basel 3.1 permissions page (updated 5 August 2026) explains how existing IRB permissions are varied for these limits.

In the EU

Regulation (EU) 2024/1623 follows Basel in removing the IRB approach for equity exposures (recital 27). Dates are in L4.1.08: Basel 3.1 from 2027: UK, EU and US.

In the US

Large US banks under the advanced approaches compute their ratios on both the standardised and the advanced approaches and must meet the minimums on each (12 CFR 217.10). Where the US stands on Basel 3.1 is in L4.1.08: Basel 3.1 from 2027: UK, EU and US.

Spark Atoms

Spark AtomThe loan that looks too safe

Own PD 0.03%, own LGD 15%, a 10% CCF and six months to run: the bank's inputs give £1.94m of RWA on a £100m drawn, £100m undrawn line. Every floor binds, and A-IRB gives £7.48m, almost four times as much. F-IRB, with its 40% LGD and 2.5 years, gives £24.45m.

Spark AtomWhen the floor bites

Take away Pellcourt's downturn add-on and its own LGD falls to 10.9%. The blended floor, 10% on the 90% secured by property and 25% on the rest, is 11.5%. It binds, and RWA rise from £640.4m to £677.2m: still well below F-IRB's £1,043.2m.

Key takeaways

F-IRB: the bank estimates PD; LGD, CCFs and maturity are supervisory. A-IRB: the bank also estimates LGD, EAD and maturity. Retail IRB has no foundation version.
Approval needs the CRE36 minimum requirements, including the use test: the ratings must drive lending and risk management, not just capital.
IRB is expected across a whole asset class, phased in under an agreed roll-out plan; immaterial exposures can stay on the SA for good; and there is no voluntary way back.
Basel 3.1 removes A-IRB for corporates above €500m of revenue and for banks and other financial institutions, removes IRB for equity, and floors PD at 0.05%, unsecured LGD at 25%, EAD and maturity.
On this book A-IRB would give £8,454.3m against F-IRB's £5,919.8m for the eligible corporates, so the bank stays on F-IRB; mortgages must use retail IRB to model at all.

Reaction

Check what stuck

Question 1 · objective 3

An A-IRB bank estimates a downturn LGD of 18% on a senior unsecured loan to a mid-sized company. What LGD goes into the formula, in %?

%

Question 2 · objective 3

A revolving facility has £200m drawn and £300m undrawn. The A-IRB bank estimates a 10% CCF. What EAD goes into the formula, in £m?

£m

Question 3 · objective 2

A company's revenue is £480m. At €1.15 per pound, what is it in € millions, the figure Basel tests against €500m?

€m

Question 4 · objective 1

Which input does an F-IRB bank estimate itself?

APD onlyBPD and LGDCPD, LGD and EADDNone: all inputs are supervisory

Question 5 · objective 2

A bank's IRB models are used only to compute capital; lending decisions use a separate scorecard. What fails?

AThe use testBThe PD floorCThe roll-out planDNothing: models can be built for capital alone

Glossary

IRB approach: Internal ratings-based (IRB) approach: the bank's own rating models supply the inputs to a supervisory risk weight formula. It needs the supervisor's approval (CRE30.1).
Foundation IRB (F-IRB): Foundation IRB (F-IRB): the bank estimates PD; LGD, EAD conversion factors and maturity are set by the rules (CRE30.33).
Advanced IRB (A-IRB): Advanced IRB (A-IRB): the bank estimates PD, LGD and EAD, and maturity is measured, all within floors (CRE30.33).
Use test: Use test: the ratings and estimates must play an essential role in credit approval, risk management, internal capital allocation and governance, not just in the capital calculation (CRE36.60).
Roll-out: Roll-out: moving exposures onto IRB over time, under a plan agreed with the supervisor. Once on IRB, a bank may not go back to the SA except in extraordinary circumstances (CRE30.47–30.50).
Permanent partial use: Permanent partial use: leaving some exposures on the SA for good, with supervisory approval, because they are immaterial in size and risk (CRE30.49).
Input floor: Input floor: a minimum value for a model input, such as 0.05% for PD. If the bank's estimate is lower, the formula uses the floor (CRE32).
Supervisory slotting: Supervisory slotting: for specialised lending, banks that cannot estimate PD put each loan in one of five categories with a set risk weight (CRE30.38, CRE33).

Deep Dives & Origins

Deep Dives

Basel Committee on Banking Supervision, High-level summary of Basel III reforms, December 2017: why the Committee constrained internal models. Intermediate.
Basel Committee on Banking Supervision, CRE36: the IRB minimum requirements, from rating system design to the use test and data histories. Advanced.

Origins

Basel Committee on Banking Supervision, CRE30, paras 30.1–30.51, bis.org.
Basel Committee on Banking Supervision, CRE32, paras 32.4–32.58, bis.org.
Basel Committee on Banking Supervision, CRE36, paras 36.19, 36.57–36.61, 36.79, 36.87–36.88, bis.org.
Basel Committee on Banking Supervision, High-level summary of Basel III reforms, December 2017.
Prudential Regulation Authority, PRA Rulebook, Credit Risk: Internal Ratings Based Approach (CRR) Part, from 1 January 2027.
Prudential Regulation Authority, PS9/24, September 2024, para 1.24; PS1/26, January 2026, para 2.10.
Prudential Regulation Authority, Basel 3.1 permissions, updated 5 August 2026.
Regulation (EU) 2024/1623, Official Journal of the European Union, 2024, recital 27.
12 CFR 217.10, US Code of Federal Regulations.

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