Rating Models and Validation - Oesterreichische Nationalbank

of approximately 10 intervals should be defined. 63 The interval widths do
not necessarily have to be identical.
8. An RDFunscaled is calculated for each interval. This corresponds to the ratio
of bad cases to good cases in each score value interval of the overall sample
used in rating development.
9. Multiplication of RDFunscaled by the rating modelÕs specific scaling factor,
which is calculated as described in section 5.3.1:
RDFscaled ¼ RDFunscaled
RDFportfolio
RDFsample
10. Conversion of RDFscaled into scaled probabilities of default (PD) for each
interval.
This procedure assigns rating modelÕs score value intervals to scaled default
probabilities. In the next step, it is necessary to apply this assignment to all of
the possible score values the rating model can generate, which is done by means
of interpolation.
If rescaling is not necessary, which means that the sample already reflects the
correct average default probability, the default probabilities for each interval are
calculated directly in step 2 and then used as input parameters for interpolation;
steps 3 and 4 can thus be omitted.
For the purpose of interpolation, the scaled default probabilities are plotted
against the average score values for the intervals defined. As each individual
score value (and not just the interval averages) is to be assigned a probability
of default, it is necessary to smooth and interpolate the scaled default probabilities
by adjusting them to an approximation function (e.g. an exponential function).
Reversing the order of the rescaling and interpolation steps would lead to a
miscalibration of the rating model. Therefore, if rescaling is necessary, it should
always be carried out first.
Finally, the score value bandwidths for the individual rating classes are
defined by inverting the interpolation function. The rating modelÕs score values
to be assigned to individual classes are determined on the basis of the defined
PD limits on the master scale.
As ÒonlyÓ the data from the collection stage can be used to calibrate the overall
scoring function and the estimation of the segmentsÕ average default probabilities
frequently involves a certain level of uncertainty, it is essential to validate
the calibration regularly using a data sample gained from ongoing operation of
the rating model in order to ensure the functionality of a rating procedure (cf.
section 6.2.2). Validating the calibration in quantitative terms is therefore one
of the main elements of rating model validation, which is discussed in detail in
chapter 6.
63 In the case of databases which do not fulfill these requirements, the results of calibration are to be regarded as statistically
uncertain. Validation (as described in section 6.2.2) should therefore be carried out as soon as possible.
Rating Models and Validation
Guidelines on Credit Risk Management 87