Suppose that the assets of an OECD bank consist of $400 million of loans to A-rated corporations. The PD for the corporations is estimated as 0.5%. The average maturity is four years and the LGD is 70%.
(a) What is the total risk-weighted assets for credit risk under the Basel II advanced IRB approach?
(b) How much Tier 1 and Tier 2 capital is required?
(c) How does this compare with the capital required under the Basel II standardized approach and under Basel I?
Exposure at Default, EAD = $400 mn, PD = 0.5%, maturity , T = 4 years
LGD = 70%
As per the IRB advanced approach, Basel II
RWA = K*12.5* EAD, where K = LGD *(N((1-R)-0.5 *G(PD) + (R/(1-R))0.5 *G(0.999) - PD) * (1+(M -2.5)*b/(1-1.5b)
On calculation, we get R = 0.267
similarly b = (0.11852-0.05478*(ln(PD)))2 = 0.167
Now, from eqn for K,
We will get K = 70%* 0.9649* 1.22 = 0.826
RWA = 0.826*12.5* 400 = $4130 million
Capital required = 8%*4130 = $330.4 mn
As per standardized approach the capital required = 50% *400 = $200 mn
We can see that as per IRB approach the capital required is much higher compared to capital calculated in standardized approach, hence giving extra cushion to the bank.
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