statistique, théorie et gestion de portefeuille - Docs at ISFA

ρ
1
0.8
0.6
0.4
0.2
0
−0.2
−0.4
−0.6
−0.8
λ ν (ρ) = 1%
λ ν (ρ) = 2.5%
λ ν (ρ) = 5%
λ ν (ρ) = 10%
−1
0 10 20 30 40 50
ν
60 70 80 90 100
Figure 2: Maximum value of the correlation coefficient ρ as a function of ν, below which the tail
dependence λν(ρ) of a Student’ copula is smaller than a given small value, here taken equal to
λν(ρ) = 1%, 2.5%, 5% and 10%. The choice λν(ρ) = 5% for instance corresponds to 1 event in 20
for which the pair of variables are asymptotically coupled. At the 1 − λν(ρ) probability level, values of
λ ≤ λν(ρ) are undistinguishable from 0, which means that the Student’s copula can be approximated by
a Gaussian copula.
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