  Vine copulas are a type of multivariate dependence model, composed of a
collection of bivariate copulas that are combined according to a specific
underlying graphical structure. Their flexibility and practicality in moderate
and high dimensions have contributed to the popularity of vine copulas, but
relatively little attention has been paid to their extremal properties. To
address this issue, we present results on the tail dependence properties of
some of the most widely studied vine copula classes. We focus our study on the
coefficient of tail dependence and the asymptotic shape of the sample cloud,
which we calculate using the geometric approach of Nolde (2014). We offer new
insights by presenting results for trivariate vine copulas constructed from
asymptotically dependent and asymptotically independent bivariate copulas,
focusing on bivariate extreme value and inverted extreme value copulas, with
additional detail provided for logistic and inverted logistic examples. We also
present new theory for a class of higher dimensional vine copulas, constructed
from bivariate inverted extreme value copulas.
