3.4 INTERNAL RATINGS–BASED MODELS FOR CREDIT RISK. Under the IRB ap-
proaches,^33 each bank is required to establish an internal ratings model to classify the
credit risk exposure of each activity (e.g., commercial lending, consumer lending,
etc.), whether on or off the balance sheet. For the Foundation IRB Approach, the re-
quired outputs obtained from the internal ratings model are estimates of one-year^34
probability of default (PD) and EAD for each transaction. In addition to these esti-
mates, independent estimates of both the loss given default (LGD) and maturity
(M)^35 are required to implement the Advanced IRB Approach. The bank computes
risk weights for each individual exposure (e.g., corporate loan) by incorporating its
estimates of PD, EAD, LGD, and M obtained from its internal ratings model and its
own internal data systems. The model also assumes that the average default correla-
tion among individual borrowers is between 10 and 20% with the correlation a de-
creasing function of PD; see BIS (2001e).^36
Expected losses upon default can be calculated as follows:
where PD is the probability of default and LGD is the loss given default.^37 However,
this considers only one possible credit event—default—and ignores the possibility
of losses resulting from credit rating downgrades. That is, deterioration in credit
quality caused by increases in PD or LGD will cause the value of the loan to be writ-
ten down—in a mark-to-market sense—even prior to default, thereby resulting in
portfolio losses (if the loan’s value is marked to market). Thus, credit risk measure-
ment models can be differentiated on the basis of whether the definition of a “credit
event” includes only default (the default mode or DM models) or whether it also in-
cludes nondefault credit quality deterioration (the mark-to-market or MTM models).
The mark-to-market approach considers the impact of credit downgrades and up-
grades on market value, whereas the default mode is only concerned about the eco-
nomic value of an obligation in the event of default. There are five elements to any
IRB approach:
1.A classification of the obligation by credit risk exposure—the internal ratings
model.Expected Losses PD LGD3 • 10 BIS BASEL INTERNATIONAL BANK CAPITAL ACCORDS(^33) In this article, we focus on the BIS II regulations as applied to on-balance-sheet activities. See
Chapter 15 in Saunders and Allen (2002) for a discussion of the BIS II proposals for off-balance-sheet
activities.
(^34) As noted earlier, the use of a one year time horizon assumes that banks can fully recapitalize any
credit losses within a year. Carey (2001b) argues that a two- to three-year time horizon is more realistic.
(^35) Maturity is the Weighted Average Life of the loan (i.e., the percentage of principal repayments in
each year times the year(s) in which these payments are received). For example, a two year loan of $200
million repaying $100 million principal in year 1 and $100 million principal in year 2 has a Weighted Av-
erage Life (WAL) = [1 (100/200)] + [2 (100/200)] = 1.5 years.
(^36) According to Carey (2001b), the January 2001 IRB proposal is calibrated to a 4.75% Tier 1 capital
ratio with a Tier 2 subordinated debt multiplier of 1.3 and a PD error multiplier of 1.2. This results in a
target capital ratio minimum of 4.75 1.3 1.2 = 7.4%. Since the BIS I 8% ratio incorporates a safety
factor for operational risk, it makes sense that the pure credit risk IRB minimum capital requirement
would be calibrated to a number less than 8%.
(^37) The format of the IRB approaches is to use PD, LGD and M to determine the loan’s risk weight and
then to multiply that risk weight times the EAD times 8% in order to determine the loan’s capital re-
quirement.