Rating Models and Validation - Oesterreichische Nationalbank

Rating Models and Validation
Chart 53: Curve of the Cumulative Probabilities Functions of Good/Bad Cases in the Data Example
The density functions show a substantial difference between good and bad
cases. The cumulative frequencies show that approximately 70% of the bad
cases — but only 20% of the good cases — belong to classes 6 to 10. On the other
hand, 20% of the good cases — but only 2.3% of the bad cases — can be found in
classes 1 to 3. Here it is clear that the cumulative probability of bad cases is
greater than that of the good cases for almost all rating classes when the classes
are arranged in order from bad to good. If the rating classes are arranged from
good to bad, we can simply invert this statement accordingly.
a and b errors
a and b errors can be explained on the basis of our presentation of density functions
for good and bad cases. In this context, a caseÕs rating class is used as the
decision criterion for credit approval. If the rating class is lower than a predefined
cutoff value, the credit application is rejected; if the rating class is higher
than that value, the credit application is approved. In this context, two types of
error can arise:
— a error (type 1 error): A case which is actually bad is not rejected.
— b error (type 2 error): A case which is actually good is rejected.
In practice, a errors cause damage due to credit defaults, while b errors
cause comparatively less damage in the form of lost business. When the rating
class is used as the criterion for the credit decision, therefore, it is important to
define the cutoff value with due attention to the costs of each type of error.
Usually, a and b errors are not indicated as absolute numbers but as percen-
tages. a error refers to the proportion of good cases below the cutoff value, that
is, the cumulative frequency F good
cum of good cases starting from the worst rating
class. a error, on the other hand, corresponds to the proportion of bad cases
above the cutoff value, that is, the complement of the cumulative frequency
of bad cases F bad
cum.
102 Guidelines on Credit Risk Management