statistique, théorie et gestion de portefeuille - Docs at ISFA

1.4
1.2
1
0.8
0.6
0.4
0.2
0 1 2 3 4 5 6 7
x 10 −3
0
log−return x
10 1
10 0
10 −1
10 −2
10 −5
10 1
10 0
10 −1
10 −3
y ∼ x 0.54
10 −4
10 −2
log−return x
y ∼ x 0.77
Figure 12: Upper panel: Sample tail (continuous line), local index β(x) (dashed line) and local exponent c(x)
(dash-dotted line) for the negative tail of the Nasdaq five minutes returns. Lower panel: doubled logarithmic
plot of the local index β(x). Over most of the data set, β(x) increases with the log-return x as a power law
of index 0.77 while beyond the quantile 99% (see the inset) it behaves like another power law of a smaller
index equal to 0.54. The goodness of fit with these two power laws has been checked by a χ 2 test.
69
10 −3
10 −2
133