  We propose a novel probabilistic model to facilitate the learning of
multivariate tail dependence of multiple financial assets. Our method allows
one to construct from known random vectors, e.g., standard normal,
sophisticated joint heavy-tailed random vectors featuring not only distinct
marginal tail heaviness, but also flexible tail dependence structure. The
novelty lies in that pairwise tail dependence between any two dimensions is
modeled separately from their correlation, and can vary respectively according
to its own parameter rather than the correlation parameter, which is an
essential advantage over many commonly used methods such as multivariate $t$ or
elliptical distribution. It is also intuitive to interpret, easy to track, and
simple to sample comparing to the copula approach. We show its flexible tail
dependence structure through simulation. Coupled with a GARCH model to
eliminate serial dependence of each individual asset return series, we use this
novel method to model and forecast multivariate conditional distribution of
stock returns, and obtain notable performance improvements in multi-dimensional
coverage tests. Besides, our empirical finding about the asymmetry of tails of
the idiosyncratic component as well as the market component is interesting and
worth to be well studied in the future.
