Advances in Risk Management

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Table 7.9 10-years Merton model

ρ 0.01 0.1 0.3 0.4 0.6 0.7 0.9 0.95

Q 99 % quantile of order 99% 1,193 1,254 1,543 1,827 2,357 2,664 3,537 3,757
E(losses|losses>q99%) 1,253 1,339 1,663 2,020 2,704 3,089 4,145 4,426
skewness 0.15 0.22 0.46 0.75 1.05 1.20 1.53 1.5
kkurtosis 2.95 3.08 3.15 3.68 4.50 4.78 5.87 6.42
average correlation (%) 10"^3 0.24 2.26 4.19 10.62 15.62 31.60 37.72

Table 7.105-years default events correlations in the intensity model,

withα=1 (%)

AAA AA A BBB BB B CCC

AAA 0.04 0.05 0.08 0.16 0.30 0.36 0.31

AA 0.05 0.08 0.12 0.24 0.44 0.55 0.53

A 0.08 0.12 0.18 0.39 0.71 0.93 0.94

BBB 0.16 0.24 0.39 0.84 1.57 2.14 2.22

BB 0.30 0.44 0.71 1.57 3.02 4.19 4.31

B 0.36 0.55 0.93 2.14 4.19 6.24 7.34

CCC 0.31 0.53 0.94 2.22 4.31 7.34 13.01

Table 7.1120-years default events correlations in the intensity model,

withα=1 (%)

AAA AA A BBB BB B CCC

AAA 0.13 0.07 0.12 0.23 0.29 0.33 0.26

AA 0.07 0.49 0.44 0.57 1.10 0.93 0.27

A 0.12 0.44 0.48 0.67 1.07 1.02 0.47

BBB 0.23 0.57 0.67 1.06 1.59 1.65 1.11

BB 0.29 1.10 1.07 1.59 3.03 2.99 2.04

B 0.33 0.93 1.02 1.65 2.99 3.46 3.41

CCC 0.26 0.27 0.47 1.11 2.04 3.41 8.39

Table 7.12 10-years intensity-based model

Var(Z)= 1 /α 0.01 0.1 0.5 2 5 10 50 100

quantile of order 99% 1190 1209 1283 1508 1766 2015 2722 3026
E(losses|losses>q99%) 1256 1275 1364 1621 1897 2178 3003 3333
skewness 0.16 0.14 0.15 0.31 0.41 0.52 0.87 0.99
kkurtosis 2.99 2.98 2.96 2.89 2.72 2.63 2.87 3.16
average correlation (%) 0.01 0.09 0.44 1.68 3.82 6.72 18.24 24.17