  Nested Archimedean copulas recently gained interest since they generalize the
well-known class of Archimedean copulas to allow for partial asymmetry.
Sampling algorithms and strategies have been well investigated for nested
Archimedean copulas. However, for likelihood based inference it is important to
have the density. The present work fills this gap. A general formula for the
derivatives of the nodes and inner generators appearing in nested Archimedean
copulas is developed. This leads to a tractable formula for the density of
nested Archimedean copulas in arbitrary dimensions if the number of nesting
levels is not too large. Various examples including famous Archimedean families
and transformations of such are given. Furthermore, a numerically efficient way
to evaluate the log-density is presented.
