Rating Models and Validation - Oesterreichische Nationalbank

Rating Models and Validation
In addition, it is necessary to pay attention to the default criterion used by
the external source. If this criterion does not match the one used in the process
of developing the rating model, it will be necessary to adjust estimates of the
segmentÕs average default rate. If, for example, the external information source
deviates from Basel II guidelines and uses the declaration of bankruptcy as the
default criterion, and if the Òloan loss provisionÓ criterion is used in developing
the model, the segmentÕs estimated average default probability according to the
external source will have to be adjusted upward. This is due to the fact that not
every loan loss provision leads to bankruptcy and therefore more loan loss provision
defaults than bankruptcy defaults occur.
Sample default rates are not scaled directly by comparing the default probabilities
in the sample and the portfolio, but indirectly using relative default frequencies
(RDFs), which represent the ratio of bad cases to good cases in the
sample.
RDF is directly proportional to the general probability of default (PD):
RDF ¼ PD
1 PD
or PD ¼ RDF
1 þ RDF
The process of rescaling the results of logistic regression involves six steps:
1. Calculation of the average default rate resulting from logistic regression
using a sample which is representative of the non-defaulted portfolio
2. Conversion of this average sample default rate into RDFsample
3. Calculation of the average portfolio default rate and conversion into
RDFportfolio
4. Representation of each default probability resulting from logistic regression
as RDFunscaled
5. Multiplication of RDFunscaled by the scaling factor specific to the rating
model
RDFscaled ¼ RDFunscaled
RDFportfolio
RDFsample
6. Conversion of the resulting scaled RDF into a scaled default probability.
This makes it possible to calculate a scaled default probability for each
possible value resulting from logistic regression. Once these default probabilities
have been assigned to grades in the rating scale, the calibration is complete.
5.3.2 Calibration in Standard Cases
If the results generated by the rating model are not already sample-dependent
default probabilities but (for example) score values, it is first necessary to assign
default probabilities to the rating results. One possible way of doing so is outlined
below. This approach includes rescaling as discussed in 5.3.1).
7. The rating modelÕs value range is divided into several intervals according to
the granularity of the value scale and the quantity of data available. The
intervals should be defined in such a way that the differences between the
corresponding average default probabilities are sufficiently large, and at
the same time the corresponding classes contain a sufficiently large number
of cases (both good and bad). As a rule, at least 100 cases per interval are
necessary to enable a fairly reliable estimate of the default rate. A minimum
86 Guidelines on Credit Risk Management