Processing Credit Risk (Basel II)
Basel II prescribes specific algorithms for the calculation of risk-weighted assets and subsequently the capital that needs to be reserved against those assets. Generally these calculations take as inputs the probability of default for the asset class, the expected exposure to the bank at the time of default, and the loss given a default (after recovery) as a percentage of the outstanding credit.
To illustrate, this is an example of the calculation for risk-weighted assets defined by Basel II. (PD and LGD are measured as decimals, and EAD is measured as currency, except where explicitly noted otherwise):
Correlation (R) = 0.12 * (1 − EXP (− 50 * PD)) / (1 − EXP (− 50)) + 0.24 * [1 − (1 − EXP (− 50 * PD)) / (1 − EXP (− 50))]
Maturity adjustment (b) = (0.08451 − 0.05898 * log (PD)) ⁁ 2
Capital requirement (K) = LGD * N [(1 − R) ⁁ − 0.5 * G (PD) + (R / (1 − R)) ⁁ 0.5 * G (0.999)] * (1 − 1.5 * b (PD)) ⁁ − 1 * (1 + (M − 2.5) * b (PD))
Risk-weighted assets (RWA) = K * 12.50 * EAD
Risk-Weighted Capital delivers these packaged algorithms for the calculation of risk-weighted assets:
|
Item |
Description |
|---|---|
|
RWC_BCR1 (PD, LGD, M) |
Calculates the capital requirement K with maturity adjustment. |
|
RWC_BCR2 (PD, LGD, M, S) |
Calculates the capital requirement K with firm-size adjustment. |
|
RWC_BCR3 (PD, LGD) |
Calculates the capital requirement K for residential mortgage exposures. |
|
RWC_BCR4 (PD, LGD) |
Calculates the capital requirement K for qualifying revolving exposures. |
|
RWC_BCR5 (PD, LGD) |
Calculates the capital requirement K for other retail exposures. |
For example, if you have a corporate loan with an exposure at default of 1,000,000 USD with these characteristics, the risk-weighted assets and regulatory capital under Basel II are computed as illustrated:
|
Item |
Calculation |
|---|---|
|
PD (probability of default) |
5% |
|
LGD (loss given default) |
50% |
|
M (maturity in years) |
2 |
|
K (capital requirement) |
0.153055762 |
|
RWA (risk-weighted assets) |
1,913,197 USD = 0.153055762 * 12.5 * 1,000,000 USD |
|
Regulatory capital (RWA * 8%) |
153,056 USD = 1,913,197 USD * .08 |