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CRR III · Basel III · ECB / SSM · Irish Banking

Internal Ratings-Based
Framework

A comprehensive explainer of the IRB approach to credit risk capital — covering Foundation vs. Advanced IRB, the capital formula, PD/LGD/EAD modelling, model governance, the output floor, and worked examples in the Irish bank context.

IRB Overview

The Internal Ratings-Based (IRB) approach allows banks to use their own statistical models — rather than fixed regulatory weights — to estimate the credit risk of their loan portfolios and calculate the minimum capital they must hold. It is the most sophisticated of the three approaches available under the Basel III / CRR framework, and the one used by the largest Irish banks.

The Problem IRB Solves

Blunt Standardised Weights

Under the Standardised Approach, a 75% risk weight applies to all retail exposures regardless of whether the borrower has a perfect credit history or is already in arrears. IRB allows banks with sophisticated risk models to use their own data-driven PD, LGD and EAD estimates, producing capital requirements that better reflect the actual risk of each portfolio.

What IRB Produces

Risk-Sensitive Capital

IRB feeds PD, LGD and EAD into a supervisory formula (the Basel asymptotic single risk factor model) that produces a risk weight for each exposure. High-quality exposures with low PD attract lower capital requirements; riskier exposures attract higher. The aggregate RWA determines the bank's minimum capital requirement.

The Regulatory Bargain

Permission vs. Constraint

Using IRB is not automatic — banks must obtain ECB permission for each model, demonstrate their models are accurate and consistently applied, and pass ongoing validation standards. In return they may hold significantly less capital than the Standardised Approach on high-quality portfolios. The output floor (CRR III) now caps the total benefit.


The Three IRB Inputs

RWA = f(PD, LGD, EAD, M) — The IRB Building Blocks
RWA = EAD × RW(PD, LGD, M, R)
PD — Probability of Default
1-year probability the obligor defaults. Through-the-cycle estimate for IRB capital (unlike IFRS 9 which uses point-in-time). Minimum floor: 0.03% for non-defaulted exposures under CRR.
LGD — Loss Given Default
Proportion of EAD expected to be lost if default occurs, net of collateral and recoveries. Under F-IRB, supervisory LGD values are prescribed. Under A-IRB, the bank estimates its own LGD subject to floors.
EAD — Exposure at Default
Expected outstanding balance at default. Under F-IRB, regulatory CCFs are applied to undrawn commitments. Under A-IRB, the bank estimates its own CCFs from historical data.

IRB in the Basel Capital Framework

FrameworkIntroducedKey IRB Change
Basel II (2004)2007–2008First introduction of IRB — Foundation and Advanced approaches. Banks could hold significantly less capital than SA if models were approved.
Basel II.5 / CRR I2011–2014Added trading book and securitisation capital charges. IRB corporate models largely unchanged but supervisory scrutiny increased post-crisis.
Basel III / CRR II2014–2021Capital quality requirements; leverage ratio; LCR/NSFR. IRB models subject to targeted review (TRIM) by ECB from 2016.
Basel III finalisation / CRR III2025–2030Output floor (72.5% of SA) phases in — caps total RWA benefit of IRB. A-IRB removed for certain exposure classes. LGD and PD floors tightened. Most significant IRB reform in 20 years.

SA vs. F-IRB vs. A-IRB

Banks choose their credit risk measurement approach on a portfolio-by-portfolio basis, subject to regulatory permission. The choice determines how much internal modelling the bank does and how much it relies on supervisory parameters.

Standardised Approach
SA
No models required

Fixed regulatory risk weights prescribed by CRR. No bank-specific modelling. External ratings (where available) may influence the weight.

  • Retail: 75% RW
  • Residential mortgage: 20–75% depending on LTV
  • Corporate: 100% (unrated); 20–150% (rated)
  • SME: 85% (retail SME); 75% (corporate SME)
Who uses SA Smaller Irish banks, credit unions, and non-bank lenders. PTSB uses SA for some portfolios. All banks must use SA as the basis for the output floor calculation under CRR III.
Foundation IRB
F-IRB
Bank estimates PD only

Bank builds and uses its own PD models (approved by ECB). LGD and CCF/EAD values are prescribed by supervisory rules, not modelled by the bank.

  • PD: bank's own approved models
  • LGD: supervisory values (45% unsecured senior; 75% subordinated; lower for collateralised)
  • CCF: regulatory values (75% for revolving committed facilities)
  • M: standard 2.5 years assumed
Under CRR III F-IRB remains available for corporate exposures. The distinction between F-IRB and A-IRB has been simplified — A-IRB is now restricted from certain exposure classes (large corporates, financial institutions) where data quality is questioned.
Advanced IRB
A-IRB
Bank estimates PD, LGD & EAD

Bank builds and uses approved models for all three inputs — PD, LGD, and EAD/CCF. The most capital-efficient approach but requires the most data and model infrastructure.

  • PD: bank's own approved models
  • LGD: bank's own approved models (subject to floors)
  • CCF: bank's own approved models
  • M: estimated from contractual cashflows (1–5 years)

What Each Approach Allows Banks to Model

ParameterStandardised (SA)Foundation (F-IRB)Advanced (A-IRB)
PDFixed regulatory weight (no PD)Own model — ECB approvedOwn model — ECB approved
LGDEmbedded in RWSupervisory values (prescribed)
EAD / CCFEmbedded in RWRegulatory CCFs
Maturity (M)Not applicableStandard 2.5 years
Capital formulaFixed weights × EADBasel supervisory formula
Minimum data historyNone5 years PD data
CRR III — A-IRB restrictions from 2025 Under CRR III, A-IRB is no longer permitted for exposures to large corporates (consolidated revenue > €500m), financial institutions, and sovereign/central government exposures. Banks using A-IRB for these classes must transition to F-IRB or SA. For Irish banks this affects a portion of their wholesale book but not their domestic retail mortgage or SME portfolios where A-IRB is retained.

The IRB Capital Formula

The Basel IRB capital formula is based on the Asymptotic Single Risk Factor (ASRF) model — a mathematical framework that derives the probability of a large unexpected loss on a portfolio given a single systematic risk factor (the state of the economy). Understanding the formula is essential to understanding why IRB risk weights behave as they do.

Basel IRB Supervisory Formula — Unexpected Loss Capital Requirement
K = LGD × [N(√(1/(1−R)) × G(PD) + √(R/(1−R)) × G(0.999)) − PD] × MA
N( ) and G( )
N = standard normal CDF; G = inverse standard normal. These map PD into the tail probability distribution used to estimate unexpected loss at the 99.9th percentile confidence interval.
R — Asset Correlation
The assumed correlation between an individual obligor's asset value and the systematic (economy-wide) factor. Higher R means the portfolio is more sensitive to economic cycles. Prescribed by Basel for each exposure class — not estimated by the bank.
MA — Maturity Adjustment
= (1 + (M − 2.5) × b(PD)) / (1 − 1.5 × b(PD)) where b(PD) = (0.11852 − 0.05478 × ln(PD))². Adjusts capital upward for longer-dated exposures to reflect greater deterioration risk over time.
What K represents K is the capital requirement as a percentage of EAD — the proportion of the exposure the bank must hold in capital to absorb unexpected losses at a 99.9% confidence level over a one-year horizon. RWA = K × EAD × 12.5. The 12.5 multiplier converts the capital percentage back into a risk-weighted asset figure (since minimum capital = 8% × RWA, and 1/8% = 12.5).

Asset Correlation (R) — The Most Misunderstood Parameter

R is not estimated by the bank — it is prescribed by Basel for each exposure class. It represents how correlated each borrower's default probability is with the overall economy. A higher R means a more concentrated portfolio where losses cluster in economic downturns.

Exposure ClassAsset Correlation (R)Formula / Note
Corporate (general)12–24%R = 0.12×(1−e−50×PD)/(1−e−50) + 0.24×(1−(1−e−50×PD)/(1−e−50)). Decreases as PD rises — high-PD obligors are more idiosyncratic.
Retail — Residential Mortgage15% (fixed)Fixed correlation reflecting the systematic nature of property price cycles. High correlation vs. other retail — house prices move together across borrowers.
Retail — Qualifying Revolving4% (fixed)Low correlation — consumer credit card defaults are more idiosyncratic; diversification benefit is highest here.
Retail — Other (SME retail)3–16%PD-dependent formula similar to corporate but with different parameters. Irish SME retail uses this class.
SME Corporate (revenue <€50m)12–24% less size adj.Same as corporate formula but with a size adjustment that reduces R for small firms — they are less correlated with the macro cycle than large corporates.
Why this matters practically The fixed 15% correlation for mortgages means that even a well-performing Irish mortgage book with very low PD still requires meaningful capital because the model assumes correlated losses in a stress scenario — the 2008 Irish experience showed this assumption was well-founded. Low-PD mortgages are not as capital-light as their PD alone might suggest.

Interactive RWA Calculator

Enter PD, LGD and select the exposure class to see the IRB risk weight and capital requirement. The formula is the full Basel supervisory formula — not an approximation.

PD — Probability of Default (%)
1.50% annual PD
LGD — Loss Given Default (%)
35% net of recoveries
EAD — Exposure at Default
k = €5.0m
Effective Maturity — years (corporate only)
2.5 years
Exposure Class
Corporate SME / Large
Asset Correlation (R)
18.2%
Prescribed by Basel for this exposure class and PD
Capital Requirement (K)
6.8%
% of EAD (99.9th pct unexpected loss)
IRB Risk Weight
85.0%
= K × 12.5
RWA
€85.0m
= RW × EAD
CET1 Capital Required (13.5%)
€11.5m
= RWA × 13.5%
SA Risk Weight (comparison)
100%
Capital saving vs. SA
Risk Weight vs. PD — IRB vs. Standardised (current LGD & class)

The Formula in Plain English

The IRB capital formula contains several mathematical functions that can look intimidating. This tab explains each one in plain language with simple everyday examples — no prior maths knowledge required.

01
The Normal Distribution — N( )
What does N(x) mean and why does it appear in the formula?

The normal distribution is the famous "bell curve". If you measured the heights of 10,000 Irish adults, most would cluster around the average (say 175cm), with fewer and fewer people at the extremes (very tall or very short). That bell-shaped pattern is a normal distribution.

The function N(x) — called the cumulative normal distribution — answers the question: "What proportion of the population sits at or below value x?" It always returns a number between 0 and 1 (a probability).

Simple example If test scores are normally distributed with average 50, N(50) = 0.5 — exactly half the students scored 50 or below. N(70) might be 0.97 — 97% scored 70 or below. N(30) might be 0.03 — only 3% scored 30 or below.

In the IRB formula, N(...) converts a combined stress score into a conditional default probability — the probability of default given that the economy is in a severe stress scenario. The output is always between 0% and 100%.

02
The Inverse Normal — G( ) or N⁻¹( )
Running the bell curve backwards

G(p) is simply the reverse of N(x). Instead of asking "what proportion sits below x?", it asks: "If p proportion of the population sits below this point, what is the point?"

Simple example If N(70) = 0.97 (97% of students scored below 70), then G(0.97) = 70. You're running the question backwards: give me the score that corresponds to being in the 97th percentile.

In the formula, G(PD) converts the bank's estimated PD (a probability like 1.5%) into a position on the normal curve. A PD of 1.5% maps to approximately G(0.015) = −2.17 — meaning this obligor sits 2.17 standard deviations below the point where defaults become the norm.

And G(0.999) is used to represent the 99.9th percentile stress scenario — a once-in-a-thousand-year economic shock. It equals approximately 3.09. This is the level of systemic stress the bank must be able to survive.

What 99.9% confidence means The formula is designed so the bank holds enough capital to survive all but the worst 0.1% of outcomes. Imagine ranking all possible economic years from best to worst — the bank needs capital to survive everything except the single worst year in a thousand.
03
Asset Correlation — R
How connected are borrowers to each other and to the economy?

R measures how much individual borrowers' fortunes move together with the overall economy. If R is high, borrowers tend to default at the same time (in a recession). If R is low, defaults are more spread out and random — one borrower defaulting tells you little about the next.

High R example — Irish residential mortgages (R = 15%) When Ireland's economy collapsed in 2008, unemployment rose, house prices fell, and mortgage defaults surged simultaneously across thousands of borrowers. The causes of default were shared — redundancy, negative equity, falling incomes. This is high correlation: one default predicted many others.
Low R example — credit cards (R = 4%) A person defaulting on their credit card because of a personal health crisis is much less likely to predict defaults by other cardholders. The causes are more individual and random. Low correlation means the portfolio benefits from more diversification.

A higher R produces a higher, fatter tail in the loss distribution — meaning the worst-case outcome is much worse than the average, and the bank needs proportionally more capital. This is why even low-PD mortgage portfolios require meaningful capital: R = 15% means correlated losses in a downturn, which is exactly what happened in Ireland.

In the formula, R appears in the expression √(R/(1−R)) × G(0.999) — this term adds the 99.9th percentile economic shock, scaled by how strongly borrowers are exposed to it. Higher R makes this term larger, increasing capital requirements.

04
The Combined Stress Term — What's Inside N( )
Putting the borrower's PD and the economy's stress together

The full expression inside N( ) is:

The combined term √(1/(1−R)) × G(PD) + √(R/(1−R)) × G(0.999)

This combines two things: the borrower's own default tendency (G(PD)) and the stress from the economy (G(0.999)). Think of it as adding up two forces pulling toward default:

  • First term √(1/(1−R)) × G(PD) — the borrower's own idiosyncratic risk, scaled up by their independence from the economy
  • Second term √(R/(1−R)) × G(0.999) — the economic shock at the 99.9th percentile, scaled by how correlated the borrower is with the economy

The result fed into N() gives the conditional default probability — the probability of this borrower defaulting given the economy is in extreme stress. This is always higher than the unconditional PD.

Concrete numbers — Irish SME, PD = 2.8%, R = 15.8% G(0.028) ≈ −1.91 (the borrower's position on the curve). G(0.999) ≈ 3.09 (the extreme stress level). Combined = √(1/0.842) × (−1.91) + √(0.158/0.842) × 3.09 = 1.090 × (−1.91) + 0.433 × 3.09 = −2.082 + 1.338 = −0.744. N(−0.744) = 0.228. So under the 99.9th percentile stress, this borrower has a 22.8% probability of defaulting — versus an unconditional PD of just 2.8%.

This dramatic jump from 2.8% to 22.8% in a stress scenario is why IRB capital requirements can look high even for moderate-risk borrowers. The formula is designed to capture the tail behaviour of a correlated portfolio under extreme stress.

05
Unexpected Loss — K = LGD × [N(...) − PD]
Why do we subtract PD? What is K actually measuring?

K is the capital requirement as a fraction of EAD. The formula subtracts PD from the stressed default probability — this is deliberate and important.

The bank already prices its expected loss (= PD × LGD × EAD) into its loan pricing and provisions — it charges a margin for the losses it expects to incur on average. Capital is only required for unexpected losses — the extra losses above and beyond what was expected that could threaten solvency.

Simple analogy An insurance company expects to pay out £10m in car claims every year. It sets its premiums to cover this. But in a bad year (motorway pile-up, flood) claims might be £35m. The company needs capital to cover the unexpected £25m excess — not the expected £10m it already planned for. IRB capital is the same: it covers the gap between stressed losses and expected losses.

So N(...) − PD = stressed default probability minus expected default probability = the unexpected default probability. Multiplied by LGD, this gives the unexpected loss rate. Multiplied by EAD, this gives the unexpected loss in cash terms, which is what the bank must hold as capital.

06
The Maturity Adjustment — MA
Why longer loans need more capital

The maturity adjustment (MA) scales capital upward for longer-dated exposures. The logic is straightforward: the longer a loan has to run, the more time there is for the borrower's credit quality to deteriorate before the bank can exit the position.

Simple example You lend money to a company for 6 months. If it starts to look shaky after 3 months, you can decline to renew and recover your money at maturity. You lend the same company money for 5 years. If it starts to look shaky after 6 months, you're stuck for another 4.5 years — the credit has more time to travel from borderline to default.

The MA formula is (1 + (M−2.5) × b) / (1 − 1.5 × b), where M is the effective maturity in years and b is a function of PD. It is anchored at 1.0 when M = 2.5 years (the standard assumption). Loans shorter than 2.5 years get a reduction; loans longer than 2.5 years get an increase.

Concrete example — 3.2 year loan at PD 2.8% b = (0.11852 − 0.05478 × ln(0.028))² = (0.11852 + 0.02478×3.576)² ≈ 0.0492. MA = (1 + (3.2−2.5) × 0.0492) / (1 − 1.5 × 0.0492) = (1 + 0.034) / (1 − 0.074) = 1.034 / 0.926 = 1.117. Capital is scaled up by 11.7% vs. a 2.5-year loan — reflecting the extra credit migration risk over the additional 0.7 years.

Retail exposures — mortgages, credit cards, personal loans — are exempt from the maturity adjustment because the Basel committee determined that retail portfolios are managed on a portfolio basis where individual loan maturities matter less than portfolio-level behaviour.

07
Putting It All Together
The formula as a single coherent story

The formula tells a single coherent story in five steps:

Start with the borrower's unconditional PD

This is the bank's best estimate of how likely this borrower is to default in a normal year — the TTC PD from the IRB model. For our Irish SME: PD = 2.8%.

Ask: what happens to this borrower in an extreme stress scenario?

Apply the asset correlation (R) and the 99.9th percentile economic shock. The borrower's default probability jumps from 2.8% to 22.8% in the stressed scenario — because they are correlated with the economy (R = 15.8%) and the economy is in severe distress.

Calculate only the unexpected part

Subtract the unconditional PD (2.8%) from the stressed default probability (22.8%) = 20.0%. This is the unexpected default rate — the part not already priced into loan margins and provisions.

Convert to a loss rate by multiplying by LGD

20.0% unexpected default rate × 38% LGD = 7.6% unexpected loss rate (pre-maturity adjustment). This is K — the capital required as a percentage of EAD.

Adjust for maturity and convert to RWA

Multiply K by the maturity adjustment (1.117 for a 3.2-year loan) = 8.5% final capital rate. Multiply by 12.5 to get the risk weight = 106%. Multiply by EAD to get RWA. Multiply RWA by 13.5% to get the CET1 capital required.

Why 12.5? The 12.5 multiplier converts K (a capital percentage) into a risk weight. It works backwards from the Basel minimum capital ratio of 8%: if a bank must hold 8% capital on every euro of RWA, then RWA = Capital / 8% = Capital × 12.5. So K × 12.5 gives the risk weight that would require exactly K capital at the 8% Pillar 1 minimum. In practice, with buffers and P2R taking the total requirement to ~13.5%, the actual capital consumed is K × EAD × 13.5%, not K × EAD × 8%.

PD Modelling for IRB

IRB PD models must estimate the through-the-cycle (TTC) probability of default over a one-year horizon for each obligor or rating grade. This is distinct from the point-in-time PD used for IFRS 9 — IRB PD must reflect the long-run average default rate across a full economic cycle, not current conditions.

TTC vs. PiT PD — The Fundamental Distinction

Through-the-Cycle (TTC) PD — IRB

Represents the long-run average default rate for a rating grade across a full economic cycle. Deliberately smoothed to prevent procyclical swings in capital requirements — if TTC PD rose and fell with the economy, banks would need most capital exactly when they can least afford it.

  • Stable over time for a given rating grade
  • Does not respond to short-term economic conditions
  • Calibrated using a long historical observation window (min. 5 years; ideally a full cycle)
  • Must include at least one period of economic stress in the calibration window
Point-in-Time (PiT) PD — IFRS 9

Reflects current economic conditions and forward-looking forecasts. Rises in recessions and falls in recoveries — deliberately procyclical because IFRS 9 wants provisions to reflect the current economic environment.

  • Volatile — changes with each macro scenario update
  • Derived from TTC PD by applying a macro adjustment scalar
  • The same BB-rated borrower: TTC PD 2.5%; PiT PD 1.0% (boom) or 6.0% (recession)
  • Used for SICR assessment and ECL calculation

Building an IRB PD Model — The Rating System

IRB banks build internal rating scales where each grade has an assigned TTC PD. The rating process maps borrower characteristics to a grade, and historical default experience for that grade establishes the PD. There are two main modelling approaches:

Statistical Scorecard

Logistic regression or similar technique maps borrower attributes (LTV, DTI, bureau score, income) to a probability score. Common for retail portfolios where volume allows statistical calibration. The score maps to a rating grade and the grade has a PD. Irish banks use scorecard models for mortgage and consumer lending.

Expert Judgement / Hybrid

For corporate and SME lending, quantitative factors (DSCR, leverage ratios, revenue trend) are combined with qualitative analyst judgement (management quality, sector outlook, competitive position). A hybrid model provides a starting point that analysts can override within documented bounds. AIB and BOI use hybrid models for their SME and mid-market corporate books.


IRB PD Requirements Under CRR / EBA

RequirementRuleIrish Bank Implication
Minimum data historyAt least 5 years of internal default data; at least 1 year of stress period includedPost-2008 Irish default data is now mature; banks had to rebuild models using crisis-era defaults which significantly raised calibrated PDs vs. pre-crisis estimates
PD floorMinimum PD of 0.03% for non-defaulted exposures under CRRPrevents artificially low PDs for very high quality exposures; most Irish retail exposures are well above this floor
Long-run average calibrationPD must represent the long-run average default rate, not a point-in-time estimateBanks must demonstrate calibration window includes stress; ECB TRIM reviews challenged models that excluded or underweighted the 2009–2012 Irish downturn
Margin of conservatism (MoC)EBA GL/2017/16 requires banks to add a margin of conservatism to PD estimates to reflect data limitations and model uncertaintySignificant uplift required where data is sparse (e.g. low-default portfolios, new product types); MoC directly increases RWA
Use testIRB ratings must be used in internal credit decisions, pricing, and risk management — not built solely for regulatory capitalBanks must demonstrate rating system is embedded in credit approval, limit setting, and risk appetite frameworks — pure "capital model" that is not used for business decisions fails the use test
Annual reviewPD models must be reviewed at least annually; significant changes require ECB notification or approvalModel lifecycle management is a significant ongoing cost; model changes that increase capital typically require notification only; changes that reduce capital require formal ECB approval

LGD Modelling for IRB

LGD is the expected proportion of an exposure lost if default occurs, after recoveries from collateral, guarantees, and obligor assets. For A-IRB, banks build their own LGD models subject to regulatory floors and stress requirements. For F-IRB, supervisory LGD values are prescribed. LGD is often the single largest driver of IRB capital for secured portfolios.

Downturn LGD — The Key IRB Requirement

IRB LGD must reflect economic downturns Under CRR, IRB LGD must reflect a downturn condition — the LGD observed when credit losses are highest in an economic cycle, not the long-run average recovery rate. For secured exposures this typically means applying stressed collateral values (lower property prices) and longer recovery timelines. Downturn LGD is always higher than long-run average LGD. The difference can be significant — Irish residential mortgage long-run average LGD might be 8%, but downturn LGD (using stressed 2009–2012 house price assumptions) could be 18–25%.
Long-Run Average LGD

Average realised LGD across the full historical observation period including all economic conditions. Used as the starting point for LGD estimation but not the final regulatory LGD — must be adjusted to reflect downturn conditions.

Downturn LGD (IRB Regulatory)

LGD calibrated to reflect stressed collateral values and extended recovery timelines during an economic downturn. EBA guidelines (GL/2019/03) require banks to identify the economic downturn period and calibrate LGD accordingly. For Irish banks this is the 2009–2012 period where property values fell 50%+ peak to trough.


LGD Floors Under CRR III

CRR III introduced binding input floors for LGD — minimum values below which a bank's own estimate cannot go regardless of its model output. These floors apply to A-IRB and prevent banks from using aggressive collateral valuations to drive LGD to near zero.

Exposure TypeLGD Floor (CRR III)Practical Impact for Irish Banks
Unsecured corporate / institutional25%Senior unsecured: many Irish corporate models were at or above this floor already given poor recovery rates post-2008
Residential real estate secured10%High-quality Irish prime mortgages (low LTV, high credit quality) had modelled LGDs below 10% before CRR III; floor now binding for this segment
Commercial real estate secured15%Irish CRE LGDs from the 2008–2012 experience were well above this floor; less binding for existing models
Unsecured retail30%Consumer and personal loans; floor generally not binding given retail LGDs are typically 40–60%
Other physical collateral secured15–20%Vehicles, plant, equipment — collateral value deterioration means LGDs above floor in most cases

Estimating LGD — The Recovery Workout Process

Default Event Identified

Bank identifies that the obligor has defaulted. The workout process begins — the bank attempts to recover as much of the outstanding exposure as possible through a combination of obligor cashflows, collateral realisation, guarantee enforcement, and legal proceedings.

Recovery Cashflows Collected

Over the resolution period (which for Irish PDH mortgages can be 3–7+ years), the bank collects all cashflows from the defaulted exposure — partial payments, property sale proceeds, guarantee recoveries. All cashflows must be discounted back to the default date at the bank's cost of capital (or contractual EIR).

Direct Costs Deducted

Legal costs, receiver fees, valuation costs, property maintenance, estate agent fees, and other direct workout costs are deducted from gross recovery proceeds. For Irish mortgage defaults these costs are substantial — legal proceedings alone can run to €20,000–€50,000 per case.

LGD = 1 − PV(Net Recoveries) / EAD

The realised LGD is the proportion of EAD not recovered in present value terms. This realised LGD feeds into the historical dataset used to calibrate the model. Banks need large samples of fully resolved defaults (i.e. workout complete) to build reliable LGD models.

Incomplete Workouts — The Irish Problem

Where a default has not yet been fully resolved (workout ongoing), the bank must estimate the final LGD using the best available information. With Irish mortgage resolution timelines often exceeding 5 years, banks have large portfolios of "work-in-progress" defaults where realised LGD is not yet known — requiring careful incomplete workout adjustments in the model calibration.

EAD & Credit Conversion Factors

Exposure at Default (EAD) is the expected outstanding balance at the time an obligor defaults. For drawn term loans it equals the current balance. For revolving facilities and undrawn commitments, a Credit Conversion Factor (CCF) must be applied to estimate how much will be drawn before default occurs — and empirical evidence shows borrowers in financial distress draw heavily on available credit before defaulting.

CCF — Why It Matters

The CCF converts an undrawn commitment into an EAD equivalent. It reflects the empirical observation that obligors approaching default draw down available revolving credit and committed facilities — often aggressively — in the period leading up to default. Ignoring this produces a material understatement of exposure.

EAD Formula
EAD = Drawn Balance + CCF × Undrawn Commitment
F-IRB CCFs (regulatory)
Unconditionally cancellable: 0%; Committed revolving (≤1yr): 20%; Committed revolving (>1yr): 50%; Other off-balance sheet: 20–100% depending on type
A-IRB CCFs (own estimates)
Bank's own empirically estimated CCFs from historical default data. Typically higher than F-IRB regulatory values — observed drawdown behaviour by distressed borrowers often exceeds regulatory assumptions.

CCF by Facility Type — Irish Bank Practice

FacilityF-IRB CCFTypical A-IRB CCFDriver
Unconditionally cancellable lines0%0–10%Bank can withdraw facility immediately; no committed exposure. However A-IRB banks observe some drawdown even on cancellable lines in practice.
Committed revolving ≤ 1yr maturity20%25–50%Short-dated committed facilities; bank obliged to fund drawdown requests until maturity
Committed revolving > 1yr50%60–85%Longer committed facilities; higher drawdown risk as bank cannot cancel for extended period; observed in Irish SME corporate data
Overdraft facilities75%65–90%High CCF — overdraft users in financial difficulty use full limit as last resort; commonly observed pre-default in Irish retail data
Credit cards75%80–95%Very high — cardholders exhaust available credit in the large majority of default cases; Irish consumer data confirms this pattern
Standby letters of credit50%BespokePerformance vs. financial letters of credit differ; probability of being called drives the EAD estimate
CRR III — CCF floors for A-IRB Under CRR III, A-IRB banks can no longer estimate CCFs below 0% (i.e. cannot assume paydowns offset drawdowns). CCF floors of 0% apply — banks cannot use negative CCFs to reduce EAD. Additionally, for revolving facilities the CRR III reforms align A-IRB CCF floors more closely with SA to prevent excessive capital reduction from own-estimate CCFs.

Model Governance & Validation

IRB model governance is as important as model accuracy. The ECB requires banks to demonstrate not only that their models produce good estimates, but that those models are subject to robust independent validation, used consistently in business decisions, and reviewed and updated regularly. Poor governance is a standalone reason for the ECB to withdraw or restrict IRB permissions.

The Three Lines of Defence

First Line — Model Development

Build & Own

The credit risk modelling team builds, documents, and maintains the IRB models. Responsible for data quality, methodology choices, calibration, and initial testing. At Irish banks this typically sits within the Chief Risk Officer function — not in business lines.

Second Line — Model Validation

Independent Challenge

An independent model validation team (separate from development) reviews every model before it goes live and annually thereafter. They assess discriminatory power, calibration accuracy, stability, and documentation quality. Findings are reported to the Model Risk Committee. ECB expects genuine independence — the validation team must be able to veto or restrict model use.

Third Line — Internal Audit

Periodic Review

Internal audit reviews the overall model governance framework — are policies followed, is validation independent, are findings acted upon? Reports to the Audit Committee. The ECB also conducts its own supervisory reviews (TRIM, targeted model investigations) which sit alongside the bank's internal governance.


Model Validation — Key Tests

TestWhat It MeasuresCommon MetricAcceptable Range
Discriminatory PowerDoes the model rank obligors correctly — do high-PD obligors default more than low-PD ones?Gini coefficient / AUROC>60% Gini (good); >70% (strong)
Calibration AccuracyAre the predicted PDs close to the observed default rates in historical data?Binomial test; Traffic light approachPredicted ≈ observed within confidence interval
Stability (PSI)Has the portfolio's score distribution shifted since the model was built? A shifted portfolio may be mis-calibrated.Population Stability Index (PSI)PSI <0.10 stable; 0.10–0.25 monitor; >0.25 investigate
Concentration RiskIs the model over-reliant on a single risk driver that could fail in specific scenarios?Variable importance; sensitivity analysisNo single variable >40% of predictive power (typical guide)
Back-testing (LGD)Do actual loss outcomes on resolved defaults match the model's predictions?Mean absolute error; coverage ratioPredicted LGD >= realised LGD (conservative)

ECB Model Approval Process — IRB Permission

Pre-Application Engagement

Bank engages informally with its Joint Supervisory Team (JST) before submitting a formal application. Flagging methodology choices and data gaps early avoids costly late-stage rejections. For a new IRB model this engagement can span 6–12 months.

Formal Application Submission

The bank submits a complete application package including: model documentation, validation report, methodology paper, data quality assessment, back-testing results, use test evidence, and governance framework documentation. The package typically runs to hundreds of pages per model.

ECB On-Site Inspection

The ECB sends examiners on-site (or conducts remote review post-COVID) to review data, systems, and governance. They interview model developers, validators, and business users. The use test is assessed here — can the bank demonstrate the model is used in credit decisions, pricing, and ICAAP?

Findings and Remediation

The ECB issues findings — classified from minor observations to material findings requiring model adjustment before approval. The bank responds with a remediation plan. For significant findings, re-submission is required. The process from application to approval typically takes 18–36 months for a complex portfolio model.

Conditional or Full Approval

The ECB grants approval — often with conditions (e.g. margin of conservatism add-on until more data is available, or a requirement to re-submit after 2 years of additional data). Conditions are recorded in the SREP decision and must be remediated within the agreed timeline.


TRIM — Targeted Review of Internal Models

The Output Floor — CRR III

The Basel III output floor is the most significant change to the IRB framework in 20 years. It caps the total capital benefit a bank can obtain from using IRB models by requiring that IRB-based RWA cannot fall below 72.5% of the RWA that would result from applying the Standardised Approach. It phases in from 2025 to 2030.

The floor in one sentence No matter how low your IRB models say your RWA is, you must hold capital on at least 72.5% of what the Standardised Approach would require on the same portfolio.

Phase-In Schedule

YearFloor LevelEffective from
202550%First year of phase-in under CRR III (EU implementation)
202655%
202760%
202865%
202970%
203072.5%Fully phased in — permanent floor

How the Floor Works — A Worked Illustration

IRB RWA (own models)
€8.0bn
Bank's A-IRB model output
SA RWA (standardised)
€14.0bn
If all exposures on SA
Floor threshold (72.5%)
€10.15bn
72.5% × €14.0bn SA RWA
Floor is binding — IRB RWA of €8.0bn is below the €10.15bn floor The bank must use €10.15bn as its RWA for capital purposes — not its own model output of €8.0bn. The difference (€2.15bn) is the "floor add-on". At 13.5% CET1 requirement this adds €290m of required capital that the bank's models say is unnecessary but the floor mandates.

Portfolio-Level Floor Impact — Irish Banks

PortfolioIRB RW (typical)SA RWFloor (72.5% × SA)Floor Binding?
Irish prime mortgage (LTV <60%)~10–15%20% (SA LTV band)14.5%Often binding — low IRB RWs
Irish prime mortgage (LTV 60–80%)~15–22%35%25.4%Frequently binding post-2025
Buy-to-let mortgage~25–45%75%54.4%Partially binding
Irish SME corporate~70–100%85–100%62–72%Rarely binding — IRB near SA
Large corporate / institutional~60–90%100%72.5%Partially binding
The key implication for Irish mortgage banks Irish banks have very low IRB risk weights on prime residential mortgages — reflecting low PDs, good collateral coverage, and the low 15% asset correlation. The output floor will force these RWAs up significantly, eroding a large part of the capital benefit that A-IRB currently provides on the mortgage book. This is a multi-year RWA headwind that both AIB and BOI have quantified explicitly in their strategic planning disclosures.

Interactive Output Floor Calculator

IRB RWA (€bn)
€8.0bn own model output
SA RWA (€bn)
€14.0bn standardised approach
CET1 Requirement (%)
13.5% incl. P2R & buffers
Floor Phase-In (%)
72.5% fully phased (2030)
Floor Threshold
€10.15bn
= floor % × SA RWA
Effective RWA
€10.15bn
max(IRB RWA, floor threshold)
Floor Add-On
€2.15bn
Additional RWA from floor
Additional Capital Required
€290m
Floor add-on × CET1 requirement
IRB Benefit Remaining
€526m
Capital saving vs. full SA
Floor Status
Binding ▲
IRB below floor threshold

Worked Examples

Two illustrative Irish exposures — a residential mortgage and an SME corporate loan — showing the full IRB capital calculation from PD/LGD/EAD inputs through the supervisory formula to final RWA and capital requirement, with comparison to the Standardised Approach.


Case A — Irish Residential Mortgage (A-IRB)

Outstanding balance
€300,000
Primary dwelling, Dublin
LTV
65%
Property value €462k
PD (TTC)
0.40%
Long-run average
LGD (downturn)
14%
Above 10% floor
StepInput / OutputNotes
EAD€300,000Fully drawn term loan — no CCF required
PD0.40%TTC PD from A-IRB mortgage model; well-seasoned prime borrower
LGD14%Downturn LGD — stressed property values, 3yr recovery time, legal costs included; above 10% floor
Asset Correlation (R)15%Fixed for residential mortgages under Basel — reflects property price cycle correlation
Maturity AdjustmentN/A (retail)Retail exposures exempt from maturity adjustment
Capital Requirement K0.97%= LGD × [N(√(1/0.85)×G(0.004) + √(0.15/0.85)×G(0.999)) − PD]
IRB Risk Weight12.1%= K × 12.5
IRB RWA€36,300= 12.1% × €300,000
SA RWA (comparison)€105,00035% SA RW for LTV 60–80% residential mortgage
Floor threshold (72.5% × SA)€76,125= 72.5% × €105,000
Effective RWA (post-floor)€76,125Floor is binding — IRB RWA (€36,300) < floor threshold (€76,125)
CET1 Required (post-floor)€10,277= €76,125 × 13.5%
CET1 Without Floor€4,901= €36,300 × 13.5% — what A-IRB model alone would produce
Floor doubles the capital requirement on this mortgage Without the output floor, A-IRB produces €4,901 capital on this €300k mortgage. The floor mandates €10,277 — more than double. This is the direct impact of CRR III on the Irish mortgage book: A-IRB model sophistication is now largely irrelevant for prime low-LTV mortgages because the SA-based floor dominates.

Case B — Irish SME Corporate Loan (A-IRB)

EAD (drawn + CCF)
€1,850,000
€1.8m drawn + CCF on €200k undrawn
PD (TTC)
2.8%
BB− internal rating
LGD (downturn)
38%
Partially secured; above 25% floor
Maturity
3.2 yrs
Effective maturity from cashflows
StepInput / OutputNotes
EAD€1,850,000€1,800,000 drawn + (75% CCF × €200,000 undrawn RCF) = €1,800,000 + €50,000 (A-IRB CCF model output; F-IRB would use 50%)
PD2.80%TTC PD from A-IRB corporate SME model; BB− grade; DSCR 1.1×, moderate leverage
LGD38%Downturn LGD — partial CRE security (€600k value); remainder unsecured; above 25% unsecured floor
Asset Correlation (R)15.8%Corporate formula: R = 0.12×(1−e−50×0.028)/(1−e−50) + 0.24×(remaining weight) ≈ 15.8%; SME size adjustment reduces R slightly vs. large corporate
Maturity Adjustment (MA)1.182M = 3.2 years; b(PD) = (0.11852 − 0.05478 × ln(0.028))² = 0.0492; MA = (1 + (3.2−2.5) × 0.0492) / (1 − 1.5 × 0.0492) = 1.182
K (pre-maturity)8.14%= LGD × [N(√(1/0.842)×G(0.028) + √(0.158/0.842)×G(0.999)) − PD]
K (post-maturity)9.62%= 8.14% × 1.182
IRB Risk Weight120.2%= 9.62% × 12.5
IRB RWA€2,224,000= 120.2% × €1,850,000
SA RWA (comparison)€2,312,50085% SME retail SA weight (if retail SME) or 100% corporate weight × EAD
Floor threshold (72.5% × SA)€1,676,563= 72.5% × €2,312,500
Floor StatusNot bindingIRB RWA (€2,224,000) > floor threshold (€1,676,563) — IRB is higher; floor does not constrain
CET1 Required€300,240= €2,224,000 × 13.5%
Floor not binding for this SME exposure Unlike the mortgage case, the SME corporate IRB RWA (€2,224,000) actually exceeds the floor threshold (€1,676,563). The output floor has no additional bite here — the bank uses its own model output directly. This reflects a key structural point: the floor is primarily a constraint on high-quality, low-RW portfolios (prime mortgages), not on riskier SME/corporate exposures where IRB weights are already substantial.

Irish Bank Context

IRB is central to how AIB and Bank of Ireland manage their capital — it determines their RWA density, capital requirements, return on equity, and the economics of their lending businesses. Understanding the Irish banks' IRB journey requires understanding the post-2008 model rebuilding, TRIM, and the CRR III headwinds now facing them.

IRB Permissions — Irish Banks

AIB Group

A-IRB Across Core Portfolios

AIB holds A-IRB permissions for residential mortgages, SME and mid-market corporate, and consumer lending. Their IRB models have been substantially rebuilt since 2008 and recalibrated following TRIM. The bank has explicitly quantified the output floor impact — estimating a multi-year RWA headwind of several billion euros as the 72.5% floor phases in on the mortgage book.

Key metricRWA density (RWA / total assets) of ~35–40% reflects the capital efficiency of A-IRB — a pure SA bank would have a materially higher density.
Bank of Ireland

A-IRB with UK Complexity

BOI holds A-IRB permissions for Irish and UK residential mortgages, corporate lending, and SME. The UK book is approved under PRA rules (which differ from ECB requirements in some areas — particularly LGD floors and downturn definitions). Maintaining parallel ECB/PRA approved models for equivalent portfolios adds significant model governance cost.

UK CRR III divergenceThe UK is implementing its own version of Basel III (the "Strong and Simple" framework and CRDVI) on a different timeline to the EU. BOI must track both regulatory regimes for its split balance sheet.
PTSB

Primarily Standardised

PTSB uses the Standardised Approach for its residential mortgage book. Building and maintaining A-IRB models requires substantial investment in data infrastructure, model teams, and ECB engagement — infrastructure that PTSB's smaller balance sheet makes harder to justify economically. The output floor has reduced the relative disadvantage of SA vs. A-IRB for mortgage books specifically.

Floor effectAs AIB and BOI's mortgage RWAs rise toward the SA floor, PTSB's SA-based capital requirements become relatively less punitive — partially levelling the competitive playing field.

The Post-2008 Model Rebuild

Irish banks had to rebuild their IRB models from scratch post-crisis Pre-2008 Irish bank IRB models were calibrated on a short and benign historical window — they had minimal default data from stress conditions. When the crisis hit, actual default rates exceeded modelled PDs by multiples. The ECB and CBI required Irish banks to recalibrate all IRB models using the 2009–2012 experience as a mandatory stress period. The effect was to significantly increase modelled PDs, LGDs, and therefore RWA across most portfolios. Some models failed minimum data requirements and had to be rebuilt entirely, requiring years of data accumulation before new models could be approved.

TRIM Findings — Irish Banks

Finding AreaCommon TRIM IssueImpact on Irish Banks
Default definitionInconsistent application — DPD resets, premature cure, inadequate UTP identificationRequired complete harmonisation with EBA GL/2016/07; historical default datasets required reconstruction; PD calibrations increased
PD calibrationInsufficient margin of conservatism; calibration window excluded or underweighted stress periodMoC add-ons applied; calibration windows extended to include 2009–2012; PDs rose materially for Irish SME and mortgage models
LGD downturnLong-run average LGD used instead of downturn LGD; recovery costs understatedDownturn LGDs increased, particularly for Irish CRE and partially secured exposures; direct capital impact
Use testIRB ratings not consistently used in credit decisions; business overrides of model ratings too frequent and poorly documentedRequired embedding of rating systems in credit approval processes; override governance frameworks strengthened
IT infrastructureModel implementation errors; inconsistent data feeds; manual adjustments without governanceSignificant IT investment required; some model approvals delayed pending system remediation

CRR III — The Capital Headwind for Irish Banks

Estimated RWA increase — AIB
+€3–5bn
Driven primarily by output floor on mortgage book (phasing 2025–2030)
Estimated RWA increase — BOI
+€2–4bn
Irish and UK mortgage floor impact; A-IRB restrictions on large corporate
CET1 impact (illustrative)
~−40–80bps
Estimated CET1 ratio reduction at full phase-in; offset by retained earnings
Management response Both AIB and BOI have factored the output floor into their capital distribution strategies — moderating buyback pacing to ensure CET1 ratios remain above targets as the floor phases in. The floor also changes the relative economics of different lending products: prime residential mortgages become less capital-efficient (floor binding), while SME and corporate lending is largely unaffected. This is already visible in pricing strategies, with tracker and prime mortgage spreads under pressure while SME lending margins remain relatively stable.

ECB & EBA Reform IRB Internal Model Approvals

A shift from ex ante to ex post — what it means for credit risk capital models. Two coordinated publications on 30 March 2026 fundamentally change how IRB credit risk model changes are approved in the EU.

In brief The ECB is switching from a pre-approval (ex ante) to a post-implementation review (ex post) model from October 2026. Simultaneously, the EBA has published revised RTS that narrow what counts as a "material" change — reducing approval traffic significantly. The combined effect is faster model improvement cycles for significant institutions.

What Problem Is Being Solved?

Under CRR, banks approved to use the Internal Ratings-Based (IRB) approach must seek supervisory approval for any material change to their credit risk models before implementing it. This applies to changes in PD, LGD, CCF models or their rating system design.

The existing regime has created a significant bottleneck. A high volume of applications for material model changes has piled up at the ECB and NCAs, causing lengthy queues. Banks have had to maintain two versions of a model — old and new — simultaneously while waiting for regulatory sign-off.

ECB Statement "By shifting from an ex ante to an ex post assessment, the ECB is making the approval process faster and more predictable for banks — allowing them to implement model changes quickly, without having to maintain old and new models in parallel."

The EBA's Revised RTS: Fewer Changes Classified as Material

The first layer of reform comes from the EBA, which has published revised Regulatory Technical Standards (RTS) on materiality assessment for IRB model changes:

Quantitative first

Greater reliance on quantitative thresholds. A change is material only if it breaches defined numerical bounds — making classification more objective and predictable.

Narrower triggers

Qualitative triggers limited to genuine redevelopments: model rebuilt from scratch, risk parameters re-estimated wholesale, or Definition of Default changes significantly.

Routine = notification

Routine model maintenance — data updates, recalibrations within thresholds — moves to notification only, unless it crosses a quantitative trigger.

CRR3 alignment

References to approaches removed under CRR3 (IRB for equity, AMA for op risk) have been deleted to align with current prudential framework.

The ECB's New Approval Process: Ex Ante → Ex Post

For material changes that still require ECB approval, the ECB is changing how it grants that approval. Effective 1 October 2026:

⛔ Old Process (Ex Ante) ✅ New Process (Ex Post)
Submit application to ECB Submit complete application package to ECB
Wait for full supervisory review (often lengthy) Internal control function confirms model compliance
Maintain old and new model in parallel throughout Bank implements change shortly after submission
Only implement change after ECB decision ECB conducts targeted post-implementation review
Every material change triggers an on-site investigation (IMI) On-site investigations reserved for higher-risk cases only
Capital floor on RWA reductions Where a change reduces risk weights, a capital floor is applied to the benefit until the ECB completes its targeted on-site review of the new model.

The Safeguards: How Resilience Is Preserved

The shift to ex post is not unconditional. Four key safeguards apply:

Internal Control Sign-off

Bank's internal control function must credibly confirm the revised model meets regulatory requirements and operational readiness.

Capital Floor on RW Reductions

Where model change results in lower risk weights, regulatory capital benefit is subject to a floor until ECB assessment.

Risk-Based On-Site Reviews

ECB on-site model investigations targeted at higher-risk cases: models with outlier behaviour, weaknesses in changing macro conditions, or flagged as sensitive.

Sensitive Case Carve-Out

For sensitive cases, ECB retains option to require standard prior approval — banks must wait for on-site investigation before implementation.

Timeline of Key Dates

30 March 2026 — Today

EBA publishes revised RTS on IRB materiality. New quantitative-first materiality criteria published. ECB simultaneously announces its new ex post supervisory approach.

1 October 2026 — Go-live

ECB's new ex post approval process takes effect. Banks may implement material credit risk model changes shortly after submitting complete application — subject to internal sign-off.

Ongoing

Targeted on-site investigations & floor releases. As ECB completes targeted reviews, capital floors can be lifted — allowing banks to fully recognise RWA benefit of improved models.

What This Means for Significant Institutions

Broader Context: "Next-Level Supervision"

This reform is explicitly part of the ECB's "Next-level supervision" project, which aims to make SSM supervision more efficient, effective and risk-based across the board. Internal model approvals were identified as one of the highest-priority areas for reform.

Other parallel strands include: streamlining SREP methodology, revising on-site inspection processes, developing tiered approach to supervisory findings, and increasing use of SupTech tools. The IRB model reform is one of the first major structural changes to become concrete and go-live.

ECB rationale This reform "builds on several years of supervisory work to make banks' internal models more reliable and consistent" — the implication being that extensive TRIM exercise and subsequent IMI campaigns have raised baseline model quality enough that ECB is comfortable moving to a more trust-based, ex post approach.

Briefing prepared from official ECB and EBA publications dated 30 March 2026. Sources: ECB Press Release 30.03.2026, EBA RTS on IRB Materiality (revised), CRR/CRR3, ECB Next-Level Supervision.