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.

本文提出一种新颖的概率模型，用于学习多元金融资产的尾部依赖，其方法可以构建新的随机向量，并且相较于常见的方法，具有更灵活、直观、易于追踪和简单抽样等优势，结合 GARCH 模型进行预测和检验，发现资产收益率的尾部具有不对称性，对此进行了初步研究。