JEAN-DAVID FERMANIAN AND MOHAMMED SBAI 145805001000150060 (^1) 0 ^1
^0
^1
^0
^1
^0
^1
40
20 2040
60
80
0
Var
80
600
1200
1800
60
1
40
20 2040
60
80
0
Expected short fall
80
4
8
12
16
20
24
2
4
6
8
10
12
60
1
40
20 2040
60
80
0
Kurtosis
80
60
1
40
20 2040
60
80
0
Mean default correlation
Figure 7.5Combined effect of the parametersα 0 andαin the multi-factor
intensity model
We lead many simulations with different values of the parametersα 0
andαiin order to study their combined effects on the loss distribution (see
Figure 7.5).
The variance ofZ 0 +Zivaries from 0.005 to 50 when (α 0 ,α) varies from
0.01 to 100, which seems to be reasonable. The levels of our dependence
indicators seem to be in line with those obtained in section 7.3. Note that we
lose some dependence when the relative importance betweenZ 0 andZiis
balanced. This is due to a diversification effect inside both components of the
frailty factors. Globally, adding an idiosyncratic frailty allow more flexibility
in the model, without losing the ability to reach realistic dependence levels.