Rating Models and Validation - Oesterreichische Nationalbank
Rating Models and Validation - Oesterreichische Nationalbank
Rating Models and Validation - Oesterreichische Nationalbank
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<strong>Rating</strong> <strong>Models</strong> <strong>and</strong> <strong>Validation</strong><br />
An ideal rating procedure would classify all actual defaults in the worst rating<br />
class. Accordingly, the ROC curve of the ideal procedure would run vertically<br />
from the lower left point (0%, 0%) upwards to point (0%, 100%) <strong>and</strong><br />
from there to the right to point (100%, 100%). The x <strong>and</strong> y values of the<br />
ROC curve are always equal if the frequency distributions of good <strong>and</strong> bad cases<br />
are identical. The ROC curve for a rating procedure which cannot distinguish<br />
between good <strong>and</strong> bad cases will run along the diagonal.<br />
If the objective is to review rating classes (as in the given example), the ROC<br />
curve always consists of linear sections. The slope of the ROC curve in each<br />
section reflects the ratio of bad cases to good cases in the respective rating class.<br />
On this basis, we can conclude that the ROC curve for rating procedures should<br />
be concave (i.e. curved to the right) over the entire range. A violation of this<br />
condition will occur when the expected default probabilities do not differ sufficiently,<br />
meaning that (due to statistical fluctuations) an inferior class will show<br />
a lower default probability than a rating class which is actually superior. This<br />
may point to a problem with classification accuracy in the rating procedure<br />
<strong>and</strong> should be examined with regard to its significance <strong>and</strong> possible causes. In<br />
this case, one possible cause could be an excessively fine differentiation of rating<br />
classes.<br />
Chart 56: Non-Concave ROC Curve<br />
a—b error curve<br />
The depiction of the a—b error curve is equivalent to that of the ROC curve.<br />
This curve is generated by plotting the a error against the b error. The a—b<br />
error curve is equivalent to the ROC curve with the axes exchanged <strong>and</strong> then<br />
tilted around the horizontal axis. Due to this property, the discriminatory<br />
power measures derived from the a—b error curve are equivalent to those<br />
derived from the ROC curve; both representations contain exactly the same<br />
information on the rating procedure examined.<br />
104 Guidelines on Credit Risk Management
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