Graphical Data Representation in Bankruptcy Analysis

Graphical Data Representation in Bankruptcy Analysis

similarity of the scores a company is assigned to one particular class. The PD
of this class becomes the PD of the company.

Fig. 3. One year probabilities of default for different rating grades [5].

Company bond ratings play an important role in determining the cost of
debt refinancing since they reflect the probability of defaulting on the debt
(Figure 3). One can notice that the differences between the classes in terms
of PDs are not the same. For example, the PD increases by 6.7% or 24 times
between classes BBB and B, but only by 0.07 or 8 times between classes AAA
und A. The colours for coding PDs must be selected so that perceptually the
classes would look equidistant, no matter what their absolute PD is. This
can be achieved by using an appropriate colour scheme and colour distance
scaling. The use of the HLS colour scheme in combination with a logarithmic
colour scaling will be demonstarated in section 6.

2 The SVM Approach

The SVM [18] is a regression (and classification) technique that is based on
margin maximisation (Figure 4) between two data classes. The margin is
the distance between the hyperplanes bounding each class where in a linear
perfectly separable case no observation may lie. The classifier function used
by the linear SVM is a hyperplane symmetrically surrounded with a margin
zone. It can be shown [9] that by maximising the margin one reduces the
complexity of such a classifier. By applying kernel techniques the SVM can
be extended to learn non-linear classifying functions (Figure 5).

In Figure 4 misclassifications are unavoidable when using linear classify-
ing functions (linearly non-separable case). To account for misclassifications

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