12
W. K. Hardle, R. A. Moro, and D. Schafer
AR (Model: SVM K*)
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32
Variable No.
Fig. 8. Accuracy ratios for univariate SVM models. Box-plots are estimated basing
on 100 random subsamples. The AR for the model containing only random variable
K10 is zero.
5 Conversion of Scores into PDs
There is another way to look at the company score. It defines the distance
between companies in terms of the distance to the boundary between the
classes. The lower is the score, the farther is a company from the class of
bankrupt companies, therefore, we can assume, the lower PD it must have.
This means that the dependence between scores and PDs is assumed to be
monotonous. This is the only kind of dependence that was assumed in all
rating models mentioned in this chapter and the only one we use for PD
calibration.
The conversion procedure consists of the estimation of PDs for the obser-
vation of the training set with a subsequent monotonisation (step one and
two) and the computation of a PD for some new company (step three).
Step one is the estimation of PDs for the companies of the training set.
We used kernel techniques to preliminary evaluate PDs for observation i from
the training set, i = 1, 2, . . . , n:
--------
PD(xi) =
П=1к Kh(xi,xj)I{yj = 1}
n=1K Kh(xi ,xj )
(11)