State-of-the-art in modeling nonlinear dependence among many random variables with copulas and application to financial indexes

In this paper, we focus our attention on multi– dimensional copula models for returns of the indexes of selected prominent international financial markets. Our modeling results, based on elliptic copulas, 7‐ dimensional hierarchical Archimedean copulas, vine co‐ pulas and factor copulas demonstrate a dominant role of the SPX index among the considered major stock indexes (mainly at the first tree of the optimal vine copulas). Some interesting weaker conditional dependencies can be de‐ tected at it’s highest trees. Interestingly, while global op‐ timal model (for the whole period of 277 months) belong to the Factor FDG copulas class, the optimal local models can be found (with very minor differences in the values of GoF test statistic) in the classes of Factor FDG and hier‐ archical Archimedean copulas. The dominance of these models is most striking over the interval of the financial market crisis, where the quality of the best Student class model was providing a substantially poorer fit.