The important question is not whether copulas work or can be made to work; of course they can (almost by construction). The important question is whether copula methods are the most intuitive way to think about dependency modeling. And that's another problem: Correlation is a linear measure of dependency; measures based on higher co-moments or nonlinear (but structurally/theoretically meaningful) functions are more useful -- especially with respect to modeling default dependencies.

Now as for copula methods, I don't like them. They obscure the dependency structure and I cannot say they do the minimal amount of abuse to what I might want to use as a baseline for dependence. Those are my major complaints against copulas. In layman's terms: I find them abstract, non-intuitive, and far too subject to noise for my comfort level.

I'd feel guilty about this; but, I did my PhD in statistics and wrote part of my dissertation on barely parametric models for dependence. So it's not like I haven't the comfort with other dependence measures or with the theory. Rather, I would prefer a model for dependence that allows me to gain even some minimal insights about the economics or risk factors in a loan portfolio.

User-friendliness might be another term for what I'm getting at: I think copulas are not so user friendly; and, since all models *are* wrong and will eventually break, I prefer methods that I can easily debug when they do break. Sure, I could do all my time series modeling with Haar wavelets and build any function from simple functions; but I don't because it doesn't give me any insights into the problem. Good models should let the data speak clearly to give the modeler those insights.

Excerpts from an interesting article in relation to the post above: Copula is one of those fashionable buzzwords (Value-at-Risk is another one), which almost no one in the financial world had heard of a few years ago, and which have now become omnipresent. Copulas are used to transform general multivariate distributions into related multivariate uniform distributions, in order to study the dependence of the modified (uniform) random variables. For some reason, this makes the analysis simpler. There are several families of copulas, used to model different types of dependencies, but the Gaussian one is by far the most popular because of its widespread adoption by the financial industry.

Li's model allowed derivatives to be rated simply on that one correlation number. An article in The Economist states ("In Plato's Cave -- Mathematical models are a powerful way of predicting financial markets. But they are fallible" -- January 22, 2009): "the [ratings] agencies’ models were even less sophisticated than the issuers’," for instance not distinguishing between a BBB rated CDO [credit debt obligation] and a BBB rated corporate bond, despite their different risk profile. The issuers were even able to "build securities with any risk profile they chose, including those made up from lower-quality ingredients that would nevertheless win AAA ratings" because they knew (thanks to third-party companies) the models the rating agencies used to rate financial instruments.

From Wired: "Just about anything could be bundled and turned into a triple-A bond—corporate bonds, bank loans, mortgage-backed securities, whatever you liked," simply by creating a derivative with the "right" correlation number. The deceptive simplicity of the model attracted quants and, more dangerously, their non-quant bosses like moths to a flame, with the results we see today.

A key issue, emphasized in the Wired article, was that the copula model assumed correlation to be constant, although in practice it varies with time and is very sensitive to small changes in the inputs. Another problem was that the historical data for the credit default swaps (CDS) covered a very narrow range of market conditions - the period during which CDS were traded witnessed soaring house prices, so models only knew a world where there was a real-estate bubble. A similar comment was made in The Economist: "there was no guarantee that the future would be like the past, if only because the American housing market had never before been buoyed up by a frenzy of CDOs."

Source: http://engineered.typepad.com/thoughts_on_business_engi/2009/03/finance-are-simple-models-bad.html