  Copulas have become an important tool in the modern best practice Enterprise
Risk Management, often supplanting other approaches to modelling stochastic
dependence. However, choosing the `right' copula is not an easy task, and the
temptation to prefer a tractable rather than a meaningful candidate from the
encompassing copulas toolbox is strong. The ubiquitous applications of the
Gaussian copula is just one illuminating example.
  Speaking generally, a `good' copula should conform to the problem at hand,
allow for asymmetry in the domain of definition and exhibit some extent of tail
dependence. In this paper we introduce and study a new class of Multiple Risk
Factor (MRF) copula functions, which we show are exactly such. Namely, the MRF
copulas (1) arise from a number of meaningful default risk specification with
stochastic default barriers, (2) are in general non-exchangeable and (3)
possess a variety of tail dependences. That being said, the MRF copulas turn
out to be surprisingly tractable analytically.
