Advances in Risk Management

136 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS Table 7.2One-year default events correlations between firms as a function of the ...

JEAN-DAVID FERMANIAN AND MOHAMMED SBAI 137 (Cox, 1972), where the (conditionally on the covariates) default intensities are mult ...

138 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS 200 0 4 8 12 16 20 24 28 600 1000 1400 Losses alpha 1 % Frequency Figure 7.2His ...

JEAN-DAVID FERMANIAN AND MOHAMMED SBAI 139 obtained in Table 7.2, especially for speculative grade firms. Nonetheless, the diffe ...

140 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS If both intensities are perfectly correlated:λA=λB=λ, then: pAB= 2 p+E ( exp ( − ...

JEAN-DAVID FERMANIAN AND MOHAMMED SBAI 141 conclude, it seems that no strong argument has been done to conclude that the correla ...

142 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS Jan-75 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 Jan-77Jan-79Jan-81Jan-83Jan-85 ...

JEAN-DAVID FERMANIAN AND MOHAMMED SBAI 143 Table 7.5 Features of the loss distribution for differentαvalues (intensity- based mo ...

144 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS 200 0 4 8 12 % Frequency 16 20 24 600 1000 1400 Losses alpha 0  0.5 et alpha  ...

JEAN-DAVID FERMANIAN AND MOHAMMED SBAI 145 80 500 1000 1500 60 
(^1)  0
^1 ^0
^1 ^0
^1 ^0
^1 40 20 2040 60 80 0 Var 80 ...

146 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS Actually, the ratior=α/α 0 provides a good measure of the dependence we obtain: ...

JEAN-DAVID FERMANIAN AND MOHAMMED SBAI 147
δ, the location parameter (Whenα>1, it measures the mean of the distribution). Th ...

148 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS in Chambers, Mallows and Stuck (1996). LetW be a random variable exponentially d ...

JEAN-DAVID FERMANIAN AND MOHAMMED SBAI 149 200 0 4 8 12 16 20 24 600 1000 1400 Losses alpha 0.8 % Frequency Figure 7.6 Histogra ...

150 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS Table 7.6 α-stable intensity-based model,T=1 year α 0.1 0.3 0.5 0.7 0.8 0.9 0.95 ...

JEAN-DAVID FERMANIAN AND MOHAMMED SBAI 151 To calculate the joint default probability of two obligors, say A and BB, with differ ...

152 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS APPENDIX B: EXTENSIONS OF THE RESULTS TO LARGE TIME HORIZONS We use the same met ...

153 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 2,3 ...

154 A COMPARATIVE ANALYSIS OF DEPENDENCE LEVELS becoming thinner and thinner when the time horizon is growing. That is why a str ...

JEAN-DAVID FERMANIAN AND MOHAMMED SBAI 155 Duffie, D. and Singleton, K. (1999) “Modeling Term Structure of Defaultable Bonds”, R ...