Advances in Risk Management

142 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS

Jan-75

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Jan-77Jan-79Jan-81Jan-83Jan-85Jan-87Jan-89Jan-91Jan-93Jan-95Jan-97Jan-99Jan-01Jan-03

Figure 7.3Monthly default rates, US bonds speculative grade,

trailing 12 months, in percents

Source: Moody’s

Table 7.4 Features of the loss distribution for differentρvalues (Merton
model),T=1 year

ρ 0.01 0.1 0.3 0.4 0.6 0.7 0.9 0.95

Quantile of order 99% 320 328 413 473 679 876 1163 1297

E(losses|losses>q99%) 356 367 482 571 858 1266 1615 1945

Skewness 0.64 0.70 1.15 1.50 2.47 4.13 4.33 5.47

Kkurtosis 3.19 3.27 4.80 6.25 13.49 35.67 29.82 49.76

Average correlation (%) 10 −^4 0.04 0.46 0.94 3.31 6.06 20.82 28.93

We led many simulations for different values of the parametersρand
α. Tables 7.4 and 7.5 summarize the results we obtained. We took the same
default probabilities and the same exposure in the two cases in order to have
the same mean distribution.
We note that the dependence indicators between default events take some
values of the same order of magnitude in the two cases. Empirically, default
event correlations are varying from 0 percent to 30 percent for the Mer-
ton model, and from 0 percent to 20 percent for the reduced-form model.
For some “reasonable”ρandαlevels (ρ= 0 .4 andα=2, for instance), the