Rating Models and Validation - Oesterreichische Nationalbank

With regard to the time interval between consecutive customer ratings, it is
necessary define a margin of tolerance for the actual time interval between rating
results for, as the actual intervals will only rarely be exactly one year. In this
context, it is necessary to ensure that the average time interval for the rating
pairs determined matches the time horizon for which the transition matrix is
defined. At the same time, the range of time intervals around this average
should not be so large that a valid transition matrix cannot be calculated.
The range of time intervals considered valid for calculating a transition matrix
should also be consistent with the bankÕs in-house guidelines for assessing
whether customer re-ratings are up to date and performed regularly.
Actual credit defaults are frequently listed as a separate class (i.e. in their
own column). This makes sense insofar as a default describes the transition
of a rated borrower to the Òdefaulted loansÓ class.
Frequently cases will accumulate along the main diagonal of the matrix.
These cases represent borrowers which did not migrate from their original
rating class over the time horizon observed. The other borrowers form a band
around the main diagonal, which becomes less dense with increasing distance
from the diagonal. This concentration around the main diagonal correlates with
the number of existing rating classes as well as the stability of the rating procedure.
The more rating classes a model uses, the more frequently rating classes
will change and the lower the concentration along the main diagonal will be.
The same applies in the case of decreasing stability in the rating procedure.
In order to calculate transition probabilities, it is necessary to convert the
absolute numbers into percentages (row probabilities). The resulting probabilities
indicate the fraction of cases in a given class which actually remained in
their original class. The transition probabilities of each row — including the
default probability of each class in the last column — should add up to 100%.
Chart 41: Empirical One-Year Transition Matrix
Especially with a small number of observations per matrix field, the empirical
transition matrix derived in this manner will show inconsistencies. Inconsistencies
refer to situations where large steps in ratings are more probable than
Rating Models and Validation
Guidelines on Credit Risk Management 89