Rating Models and Validation - Oesterreichische Nationalbank

— For all other statistical and heuristic rating models, it is necessary to assign
default probabilities in the calibration process. In such cases, it may also
be necessary to rescale results in order to offset sample effects (see section
5.3.2).
— The option pricing model already yields sample-independent default probabilities.
Chart 39: Calibration Scheme
5.3.1 Calibration for Logistic Regression
The results output by logistic regression are already in the form of default probabilities.
The average of these default probabilities for all cases in the sample
corresponds to the proportion of bad cases included a priori in the analysis sample.
If logistic regression is only one of several modules in the overall rating
model (e.g. in hybrid systems) and the rating result cannot be interpreted
directly as a default probability, the procedure described under 5.3.2 is to be
applied.
Rescaling default probabilities is therefore necessary whenever the proportion
of good and bad cases in the sample does not match the actual composition
of the portfolio in which the rating model is meant to be used. This is generally
the case when the bank chooses not to conduct a full data survey. The average
default probability in the sample is usually substantially higher than the portfolioÕs
average default probability. This is especially true in cases where predominantly
bad cases are collected for rating system development.
In such cases, the sample default probabilities determined by logistic regression
have to be scaled to the average market or portfolio default probability. The
scaling process is performed in such a way that the segmentÕs ÒcorrectÓ average
default probability is attained using a sample which is representative of the segment
(see chart 39). For example, it is possible to use all good cases from the
data collected as a representative sample, as these represent the bankÕs actual
portfolio to be captured by the rating model.
In order to perform calibration, it is necessary to know the segmentÕs average
default rate. This rate can be estimated using credit reporting information,
for example. In this process, it is necessary to ensure that external sources are in
a position to delineate each segment with sufficient precision and in line with
the bankÕs in-house definitions.
Rating Models and Validation
Guidelines on Credit Risk Management 85