statistique, théorie et gestion de portefeuille - Docs at ISFA

9.1. Les différentes mesures de dépendances extrêmes 261
ian stock index daily volatility larger than a given value v.
Figure 6: In the upper panel, the thick plain curve shows the correlation coefficient between the Chilean
stock index daily returns and the Mexican stock index daily returns conditioned on the Mexican stock index
daily returns larger than (smaller than) a given positive (negative) value v (after normalization by the standard
deviation). The thick dashed curve represents the theoretical conditional correlation coefficient ρ +,−
v
calculated for a bivariate Gaussian model, while the two thin dashed curves represent the area within which
we cannot consider, at the 95% confidence level, that the estimated correlation coefficient is significantly
different from its Gaussian theoretical value. The dotted curves provide the same information under the
assumption of a bivariate Student’s model with ν = 3 degrees of freedom.
The lower panel gives the same kind of information for the correlation coefficient conditioned on the Chilean
stock index daily returns larger than (smaller than) a given positive (negative) value v.
Figure 7: In the upper panel, the thick plain curve depicts the correlation coefficient between the Chilean
stock index daily returns and the Mexican stock index daily returns conditioned on the Mexican stock index
daily volatility larger than a give value v (after normalization by the standard deviation). The thick dashed
curve represents the theoretical conditional correlation coefficient ρ +,−
v calculated for a bivariate Gaussian
model, while the two thin dashed curves represent the area within which we cannot consider, at the 95%
confidence level, that the estimated correlation coefficient is significantly different from its Gaussian theoretical
value. The dotted curves provide the same information under the assumption of a bivariate Student’s
model with ν = 3 degrees of freedom.
The lower panel gives the same kind of information for the correlation coefficient conditioned on the Chilean
stock index daily volatility larger than a given value v.
Figure 8: Conditional Spearman’s rho for a bivariate Gaussian copula (left panel) and a Student’s copula
with three degrees of freedom (right panel), with an unconditional linear correlation coefficient ρ =
0.1, 0.3, 0.5, 0.7, 0.9.
Figure 9: In the upper panel, the thick curve shows the Spearman’s rho between the Argentina stock index
daily returns and the Brazilian stock index daily returns. Above the quantile v = 0.5, the Spearman’s rho is
conditioned on the Brazilian index daily returns whose quantiles are larger than v, while below the quantile
v = 0.5 it is conditioned on the Brazilian index daily returns whose quantiles are smaller than v. As in the
above figures for the correlation coefficients, the dashed lines refer to the prediction of the Gaussian copula
and its 95% confidence levels and the dotted lines to the Student’s copula with three degrees of freedom
and its 95% confidence levels. The lower panel gives the same kind of information for the Spearman’s rho
conditioned on the realizations of the Argentina index daily returns.
Figure 10: In the upper panel, the thick curve shows the Spearman’s rho between the Brazilian stock index
daily returns and the chilean stock index daily returns. Above the quantile v = 0.5, the Spearman’s rho is
conditioned on the Chilean index daily returns whose quantiles are larger than v, while below the quantile
v = 0.5 it is conditioned on the Mexican index daily returns whose quantiles are smaller than v. The dashed
lines refer to the prediction of the Gaussian copula and its 95% confidence levels and the dotted lines to the
Student’s copula with three degrees of freedom and its 95% confidence levels. The lower panel gives the
same kind of information for the Spearman’s rho conditioned on the realizations of the Brazilian index daily
returns.
Figure 11: In the upper panel, the thick curve depicts the Spearman’s rho between the Chilean stock index
daily returns and the Mexican stock index daily returns. Above the quantile v = 0.5, the Spearman’s rho is
conditioned on the Mexican index daily returns whose quantiles are larger than v, while below the quantile
v = 0.5 it is conditioned on the Mexican index daily returns whose quantiles are smaller than v. The dashed
lines refer to the prediction of the Gaussian copula and its 95% confidence levels and the dotted lines to the
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