FRM Exam Part II · Credit Scoring and Rating

Internal Rating Systems and Basel IRB Requirements

Updated 11 October 2026 · Fact-checked

An internal rating system assigns each borrower a grade, links each grade to a probability of default (PD), and feeds PD, LGD and EAD into Basel IRB capital formulas. To solve questions, identify the rating philosophy (TTC or PIT), the IRB approach (foundation or advanced), and which inputs the bank estimates itself.

Understand Internal Rating Systems and Basel Requirements

An internal rating system is the set of methods, data, processes and controls a bank uses to assess credit risk and assign borrowers to rating grades. Each grade groups borrowers with similar default risk. A bank builds the scale so that grades are well spread and no single grade holds too large a share of exposures.

The key output is a probability of default (PD) for each grade. A bank does this by mapping: it takes the historical default rates observed for each grade, or it links its grades to an external agency scale or a scoring model output. Basel requires PD to be a long-run average of one-year default rates for the grade. Basel also sets a PD floor. The Basel II floor was 0.03% for corporate and bank exposures. The finalised Basel III framework raises it to 0.05% for these exposures. Retail classes have their own floors, for example 0.05% for mortgages and 0.10% for QRRE revolvers.

Rating philosophy matters. A through-the-cycle (TTC) rating looks past the current economic phase, so grades are stable and migrate little. A point-in-time (PIT) rating uses current conditions, so grades and PDs move with the cycle. TTC ratings give more stable capital but less timely warning. PIT ratings are more responsive but make capital more procyclical. Most banks use a hybrid.

Under the Internal Ratings-Based (IRB) approach, a bank with supervisory approval uses its own estimates in the capital formula. In foundation IRB (F-IRB), the bank estimates PD, with supervisory LGD and EAD (through conversion factors). Maturity is generally fixed at 2.5 years, unless national supervisors permit the bank to use effective maturity. Under Basel II, the supervisory LGD for senior unsecured corporate claims was 45%. The finalised Basel III framework sets it at 40% for senior unsecured claims on non-financial corporates and 45% for those on financial institutions. In advanced IRB (A-IRB), the bank estimates PD, LGD, EAD and, where applicable, maturity. The Basel III finalisation restricted A-IRB for some exposure classes. Large corporates (consolidated revenue above €500 million) and banks and other financial institutions are limited to F-IRB. The finalisation also added input floors and an output floor.

Basel sets minimum standards for IRB use: meaningful differentiation of risk, rating of all exposures, a minimum number of grades, independent rating assignment and review, at least annual review of ratings, a data history for estimation, stress tests, validation and board and senior management oversight. The use test requires that ratings drive real decisions such as pricing and limits, not just capital.

Key formulas to remember

Expected loss: EL = PD × LGD × EAD; Covered by provisions and pricing. Under IRB, the capital requirement targets unexpected loss.
LGD and recovery: LGD = 1 − Recovery rate; Express both as a percentage of EAD. Basel requires LGD to reflect downturn conditions.
Grade PD from history: PD (grade) = Defaults in year ÷ Obligors in grade at start of year; long-run PD = average over many years; Use obligors that were in the grade at the start of the period. Use a long-run average for TTC-style estimates.
Number of defaults implied: Expected defaults = PD × Number of obligors; Useful for backtesting a grade against observed defaults.
Basel PD floor: PD ≥ 0.05% for corporate and bank exposures under the finalised Basel III framework (Basel II floor: 0.03%); Retail classes have their own floors, for example 0.05% for mortgages and 0.10% for QRRE revolvers. Defaulted exposures are assigned PD = 100%.
Basel IRB estimates by approach: F-IRB: bank estimates PD, with supervisory LGD and EAD; maturity generally fixed at 2.5 years unless national supervisors permit effective maturity. A-IRB: bank estimates PD, LGD, EAD and maturity; In F-IRB, supervisory LGD for senior unsecured corporate claims was 45% under Basel II. The finalised Basel III framework sets it at 40% for non-financial corporates and 45% for financial institutions. Large corporates (revenue above €500 million) and banks are limited to F-IRB.
IRB capital charge: Capital requirement = K × EAD; RWA = K × 12.5 × EAD; K depends on PD, LGD, maturity and asset correlation, with a 99.9% one-year confidence level; You need the structure, not the full formula. Higher PD or LGD raises K. Higher EAD raises the capital amount.

How to solve Internal Rating Systems and Basel Requirements questions

Use this sequence for any question on rating systems, PD mapping or IRB requirements.

1Identify what is asked: grade design, PD mapping, rating philosophy, IRB approach or Basel minimum requirement.
2Note the exposure class and approach. Check whether the bank is on the standardised, F-IRB or A-IRB approach.
3For PD mapping, use the grade's long-run average of one-year default rates, with obligors counted at the start of each year.
4For philosophy, ask whether the rating reacts to the cycle. Stable grades and PDs mean TTC. Fast-moving grades and PDs mean PIT.
5For expected loss or capital inputs, list PD, LGD and EAD, check units, and multiply: EL = PD × LGD × EAD.
6Match requirements to the principle: independence, annual review, data history, validation, use test, board oversight.
7State the interpretation: what it means for capital stability, procyclicality or model risk, then pick the option that fits.

Quickest way: Three-check shortcut for rating questions

When to use it: Use it for conceptual MCQs on TTC vs PIT, F-IRB vs A-IRB or Basel minimum standards.

Check 1: Who estimates what? F-IRB means bank PD only. A-IRB means PD, LGD, EAD.
Check 2: Stable or reactive? TTC is stable and less procyclical. PIT is reactive and more procyclical.
Check 3: Is the option a Basel standard? Independence, annual review, validation, use test and data history are correct. Anything that lets the business line alone set or override ratings is wrong.
For numbers, compute EL = PD × LGD × EAD or average the yearly default rates, then match one option.

Common mistakes in Internal Rating Systems and Basel Requirements

Treating TTC ratings as unaffected by borrower quality changes
The word stable is read as never changing.
Fix: TTC ratings ignore cyclical swings but still migrate when a borrower's own creditworthiness changes.
Saying PIT ratings reduce procyclicality
Students link responsive ratings with better risk measurement.
Fix: PIT PDs rise in downturns, so capital requirements rise when capital is scarce. That increases procyclicality.
Believing F-IRB banks estimate LGD and EAD
Foundation is confused with advanced.
Fix: In F-IRB the bank supplies PD only. Supervisors supply LGD and EAD conversion factors.
Computing grade PD from the end-of-year population
Defaulters leave the pool, so the wrong denominator seems natural.
Fix: Divide defaults in the year by obligors in the grade at the start of the year.
Using the average of one bad year as the long-run PD
Students take the latest data as most relevant.
Fix: Basel expects PD to be a long-run average of one-year default rates through a full cycle.
Treating ratings as only a capital tool
The IRB focus on capital hides the use test.
Fix: Remember the use test: ratings must drive credit approval, pricing, limits and provisioning.

Worked examples

Example 1

A bank's grade 4 had the following one-year outcomes at the start of each year: Year 1: 800 obligors, 16 defaults. Year 2: 1,000 obligors, 40 defaults. Year 3: 900 obligors, 9 defaults. Estimate the long-run PD for grade 4 as a simple average of annual default rates, and the expected loss in rupee terms on an exposure of ₹50,00,000 if LGD is 40%.

Show the solution

Year 1 default rate = 16 ÷ 800 = 2.0%.
Year 2 default rate = 40 ÷ 1,000 = 4.0%.
Year 3 default rate = 9 ÷ 900 = 1.0%.
Long-run PD = (2.0% + 4.0% + 1.0%) ÷ 3 = 7.0% ÷ 3 = 2.3333%.
EL = 0.023333 × 0.40 × ₹50,00,000 = ₹46,666.67, which is about ₹46,667. Rounding PD to 2.333% first would give about ₹46,660.

Answer: Long-run PD is about 2.33% and expected loss is about ₹46,667.

Example 2

A bank rates borrowers using a model that updates PD every month from equity prices and spreads. During a recession, many borrowers migrate to worse grades and the bank's IRB capital requirement rises sharply. Which rating philosophy is it, and which statement is correct? (A) TTC, because grades are stable. (B) PIT, because PDs react to current conditions, which increases procyclicality. (C) TTC, because capital falls in recessions. (D) PIT, because it uses long-run average defaults only.

Show the solution

Monthly updating from market data means PDs reflect current conditions, so the philosophy is point-in-time.
Option A is wrong because TTC grades would not move sharply with the cycle.
Option C is wrong because the capital requirement rose, and TTC would not cause this.
Option D is wrong because PIT does not use only long-run averages; that describes TTC.
Option B correctly links PIT to rising capital in a downturn, which is procyclicality.

Answer: B: PIT, because PDs react to current conditions, which increases procyclicality.

Exam tips

Expect scenario MCQs that ask you to name the rating philosophy from the way the system behaves.
Memorise the F-IRB vs A-IRB split of who estimates PD, LGD, EAD and maturity.
For Basel minimum requirements, pick answers about independence, annual review, validation, data history, stress testing and the use test.
In number questions, check the denominator for PD and that PD, LGD and EAD are in consistent units before multiplying.
Remember the link to the Basel III finalisation: input floors and an output floor limit how low IRB capital can fall.

Practice questions from Credit Scoring and Rating

Internal Rating Systems and Basel Requirements in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Internal Rating Systems and Basel Requirements: frequently asked questions

What is the difference between through-the-cycle and point-in-time ratings?

A through-the-cycle rating assesses a borrower over a full economic cycle, so it is stable and moves little with the economy. A point-in-time rating reflects current conditions, so it moves with the cycle. TTC lowers procyclicality in capital, while PIT gives earlier warning.

How do banks map internal ratings to probability of default?

Banks calculate the one-year default rate for each grade over many years and take a long-run average. They can also calibrate to external agency default studies or to scoring model outputs. The result must then be validated and meet any Basel floors.

What is the difference between foundation and advanced IRB?

In foundation IRB the bank estimates PD, while supervisors set LGD and EAD conversion factors. Maturity is fixed at 2.5 years unless national supervisors permit the bank to use effective maturity. In advanced IRB the bank estimates PD, LGD, EAD and maturity itself. Advanced IRB needs more data and stronger validation, and Basel III restricts it for some exposure classes.

What does the Basel use test require?

It requires that internal ratings and estimates play an essential role in credit approval, risk management, internal capital allocation and governance. Ratings built only to compute regulatory capital do not meet this standard.