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284 9. Mesure de la dépendance extrême entre deux actifs financiers
Bivariate Gaussian
Bivariate Student’s
√ ρ 1 ·
1−ρ2 v
ρ
ρ
2 +(ν−1)ν−2
(1−ρ ν
2 )
ρ + v ρ s v ρu
(3) 1 − 1
2
(6)
1−ρ 2
ρ 2
ρ
ρ
2 + 1
(1−ρ (ν−1)ν−2
ν
2 )
1
v2 (4) ρ 1+ρ 1
1−ρ · u2 (13)
(7) -
Gaussian Factor Model same as (3) same as (4) same as (13)
Student’s Factor Model 1 − K
v 2 (11) 1 − K
v 2 (11) -
Table 3: Large v and u dependence of the conditional correlations ρ + v (signed condition), ρ s v (unsigned
condition) and ρu (on both variables) for the different models studied in the present paper, described in the
first column. The numbers in parentheses give the equation numbers from which the formulas are derived.
The factor model is defined by (8), i.e., X = αY + ɛ. ρ is the unconditional correlation coefficient.
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