Foundation IRB Specification¶

Foundation IRB calculation with supervisory LGD, PD floors, and correlation formulas.

Regulatory Reference: CRR Articles 153-154, 161-163

Test Group: CRR-B

Requirements Status¶

Supervisory LGD Values (CRR Art. 161)¶

Under F-IRB, LGD is prescribed by the regulator based on collateral type:

PD Floor¶

CRR: Single floor of 0.03% for all exposure classes (Art. 163).

See Framework Differences for Basel 3.1 differentiated PD floors.

Asset Correlation Formula (CRR Art. 153)¶

Corporate, Institution, Sovereign¶

PD-dependent correlation with exponential decay factor of 50:

f(PD) = (1 - exp(-50 x PD)) / (1 - exp(-50))
R = 0.12 x f(PD) + 0.24 x (1 - f(PD))

SME Firm-Size Adjustment¶

For corporates with turnover < EUR 50m, correlation is reduced:

s = max(5, min(turnover_EUR, 50))
adjustment = 0.04 x (1 - (s - 5) / 45)
R_adjusted = R - adjustment

Turnover is stored in GBP and converted to EUR via the configured FX rate.

Retail Mortgage¶

Fixed correlation: R = 0.15

Qualifying Revolving Retail (QRRE)¶

Fixed correlation: R = 0.04

Other Retail¶

PD-dependent correlation with exponential decay factor of 35:

f(PD) = (1 - exp(-35 x PD)) / (1 - exp(-35))
R = 0.03 x f(PD) + 0.16 x (1 - f(PD))

FI Scalar (CRR Art. 153(2))¶

A 1.25x multiplier applied to the correlation coefficient for large or unregulated financial sector entities (per CRR Art. 153(2)).

Capital Requirement Formula¶

K = LGD x N[(1-R)^(-0.5) x G(PD) + (R/(1-R))^(0.5) x G(0.999)] - PD x LGD

Where:

• N(x) = cumulative normal distribution function
• G(x) = inverse normal CDF
• G(0.999) = 3.0902323061678132
• K is floored at 0

Maturity Adjustment (CRR Art. 162)¶

Applied to non-retail exposures only (retail exposures use MA = 1.0):

b = (0.11852 - 0.05478 x ln(PD))^2
MA = (1 + (M - 2.5) x b) / (1 - 1.5 x b)

Maturity M is clamped to the range [1.0, 5.0] years.

RWA Calculation¶

CRR: RWA = K x 12.5 x 1.06 x EAD x MA

The 1.06 is the CRR scaling factor (not present in Basel 3.1).

Expected Loss¶

EL = PD x LGD x EAD

Used for comparison against provisions (see Provisions).

Key Scenarios¶