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Extreme dependence measures based on independent component analysis

In the analysis of multidimensional extreme observations we are 
often interested in understanding the dependence structure of the 
marginals, in order to define measures to be used, for example, in 
risk management. With this aim, many models have been built using 
copula functions developed both with a nonparametric approach and 
with families of parametric models. A limit in the use of copula 
functions in this context is due to the fact that there isn't a 
finite parametric model which can express all the possible shapes of 
the multivariate extreme-value copula. In this paper we propose a 
different model to estimate the dependence structure of the extreme 
values based on the analysis of independent components with sources 
distributed as the generalized extreme-value random variable. This 
approach do not need the knowledge of the multivariate extreme-value 
distribution which could have generated sample data and put aside 
the marginals, as in copula structure analysis method; respect to 
this method, anyway, it identifies a unique dependence structure. An 
application of the model in the estimation of the value-at-risk of 
the extreme returns relating to a portfolio of assets shows the 
value of the proposed methodology.