  We propose a new method for estimating the extreme quantiles for a function
of several dependent random variables. In contrast to the conventional approach
based on extreme value theory, we do not impose the condition that the tail of
the underlying distribution admits an approximate parametric form, and,
furthermore, our estimation makes use of the full observed data. The proposed
method is semiparametric as no parametric forms are assumed on all the marginal
distributions. But we select appropriate bivariate copulas to model the joint
dependence structure by taking the advantage of the recent development in
constructing large dimensional vine copulas. Consequently a sample quantile
resulted from a large bootstrap sample drawn from the fitted joint distribution
is taken as the estimator for the extreme quantile. This estimator is proved to
be consistent. The reliable and robust performance of the proposed method is
further illustrated by simulation.
