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248 9. Mesure de la dépendance extrême entre deux actifs financiers
the Brazilian case, the estimates of the correlation coefficient will be particularly noisy and thus of weak
statistical value.
We have checked that the fat tailness of the indexes expressed in US dollar comes from the impact of the
exchange rates. Thus, an alternative should be to consider the indexes in local currency, following (Longin
and Solnik 1995) and (Longin and Solnik 2001)’s methodology, but it would lead to focus on the linkages
between markets only and to neglect the impact of the devaluations, which is precisely the main concern of
many studies about the contagion in Latin America.
Figures 2, 4 and 6 give the conditional correlation coefficient ρ +,−
v
(plain thick line) for the pairs Ar-
gentina / Brazil, Brazil / Chile and Chile / Mexico while figures 3, 5 and 7 show the conditional correlation
coefficient ρ s v for the same pairs. For each figure, the dashed thick line gives the theoretical curve obtained
under the bivariate Gaussian assumption whose analytical expressions can be found in appendices A.1.1
and A.1.2. The unconditional correlation coefficient of the Gaussian model is set to the empirically estimated
unconditional correlation coefficent. The two dashed thin lines represent the interval within which
we cannot reject, at the 95% confidence level, the hypothesis according to which the estimated conditional
correlation coefficient is equal to the theoretical one. This confidence interval has been estimated using the
Fisher’s statistics. Similarly, the thick dotted curve graphs the theoretical curve obtained under the bivariate
Student’s assumption with ν = 3 degrees of freedom (whose expressions are given in appendices B.3
and B.4) and the two thin dotted lines are its 95% confidence level. Here, the Fisher’s statistics cannot be
applied, since it requires at least that the fourth moment of the distribution exists. In fact, (Meerschaert and
Scheffler 2001) have shown that, in such a case, the distribution of the sample correlation converges to a
stable law with index 3/2, which justifies why the confidence interval for the Student’s model with three
degres of freedom is much larger than the confidence interval for the Gaussian model. In the present study,
we have used a bootstrap method to derive this confidence interval since the scale factor intervening in the
stable law is difficult to calculate.
In figures 2, 4 and 6, we observe that the change in the conditional correlation coefficients ρ +,−
v
are not sig-
nificantly different, at the 95% confidence level, from those obtained with a bivariate Student’s model with
three degrees of freedom. In contrast, the Gaussian model is often rejected. In fact, similar results hold (but
are not depicted here) for the three others pairs Argentina / Chile, Argentina / Mexico and Brazil / Mexico.
Thus, these observations should lead us to conclude that, in these cases, no change in the correlations, and
therefore no contagion mechanism, needs to be invoked to explain the data, since they are compatible with
a Student’s model with constant correlation.
Let us now discuss the results obtained for the correlation coefficient conditioned on the volatility. Figures
3 and 7 show that the estimated correlation coefficients conditioned on volatility remain consistent with the
Student’s model with three degres of freedom, while they still reject the Gaussian model. In contrast, figure
5 shows that the increase of the correlation cannot be explained by any of the Gaussian or Student models,
when conditioning on the Mexican index volatilty. Indeed, when the Mexican index volatility becomes larger
than 2.5 times its standard deviation, none of our models can account for the increase of the correlation. The
same discrepancy is observed for the pairs Argentina / Chile, Argentina / Mexico and Brazil / Mexico which
have not been represented here. In each case, the Chilean or the Mexican market have an impact on the
Argentina or the Brazilian market which cannot be accounted for by neither the Gaussian or Student models
with constant correlation.
To conclude this empirical part, there is no significant increase in the real correlation between Argentina
and Brazil in the one hand and between Chile and Mexico in the other hand, when the volatility or the
returns exhibit large moves. But, in period of high volatility, the Chilean and Mexican market may have an
genuine impact on the Argentina and Brazilian markets. Thus, a priori, this should lead us to conclude on
the existence of a contagion across these markets. However, this conclusion is based on the investigation of
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