What is the IRB approach for credit risk and how do PD, LGD, and EAD interact to determine capital requirements?

The Internal Ratings-Based (IRB) approach allows banks to use their own internal estimates of credit risk parameters to calculate regulatory capital. This gives sophisticated banks the potential for lower capital requirements if they can demonstrate strong modeling capabilities.

The Four Key Parameters:

1. PD (Probability of Default) — The likelihood that the borrower defaults within one year. Under Foundation IRB, the bank estimates PD internally. Under Advanced IRB, the bank estimates PD as well.

1. LGD (Loss Given Default) — The percentage of exposure lost if default occurs (after recovery). Foundation IRB uses supervisory LGD values (45% for senior unsecured, 75% for subordinated). Advanced IRB lets the bank estimate LGD internally.

1. EAD (Exposure at Default) — The total amount exposed at the time of default, including drawn amounts and a portion of undrawn commitments. Foundation IRB uses supervisory CCFs (credit conversion factors). Advanced IRB allows internal estimates.

1. M (Effective Maturity) — Foundation IRB assumes 2.5 years for all exposures. Advanced IRB uses the actual effective maturity.

How the Risk Weight Function Works:

The Basel IRB formula computes a risk weight based on:

• The asset correlation function R(PD) — decreases as PD increases (riskier borrowers have lower correlation with the macro economy)
• The conditional PD under a stressed scenario — using the Vasicek single-factor model
• The maturity adjustment — longer maturities receive higher capital

The formula is complex but conceptually:

Capital per unit of EAD = LGD × [Φ((1-R)^(-0.5) × Φ⁻¹(PD) + (R/(1-R))^0.5 × Φ⁻¹(0.999)) - PD] × Maturity Adjustment

Foundation vs Advanced IRB Summary:

Key Regulatory Requirements:

• Minimum 5-7 years of internal default data for PD estimation
• Complete economic cycle coverage for LGD estimation (Advanced IRB)
• Annual validation of all internal models
• Basel III introduced an output floor: IRB capital cannot fall below 72.5% of the standardized approach capital

Exam Tip: FRM II loves testing the Foundation vs Advanced distinction — know which parameters the bank estimates vs which are set by supervisors.

Deepen your Basel knowledge in our FRM Part II resources.