Advances in Risk Management

138 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS

200

0

4

8

12

16

20

24

28

600 1000 1400

Losses

alpha 1

% Frequency

Figure 7.2Histogram of the losses in an intensity-based model

Table 7.3One-year default events correlations between firms with

different ratings (%), withα= 1

AAA AA A BBB BB B CCC

AAA 0.03 0.03 0.04 0.10 0.20 0.42 0.78

AA 0.03 0.03 0.04 0.10 0.20 0.42 0.78

A 0.04 0.04 0.05 0.13 0.26 0.54 1.00

BBB 0.10 0.10 0.13 0.37 0.71 1.46 2.72

BB 0.2 0.2 0.26 0.71 1.36 2.81 5.25

B 0.42 0.42 0.54 1.46 2.81 5.84 11.00

CCC 0.78 0.78 1.00 2.72 5.25 11.00 21.79

For example, forα=1 andT=1, we get the histogram of the losses in
Figure 7.2. Such empirical distribution looks like the one obtained with the
Merton-style model (graph 1), especially in the right tail.
Again, forα=1 we calculate the default events correlations between firms
with different ratings: Table 7.3. We get levels that are comparable with those