What is copulas exactly, in probability and finance terms

Hi, all

What exactly is a copula? My understanding is: there are couple of components
1. uniform cdf marginal
2. a covariance matrix

What exactly is this thing? Why am I calculating the marginals and what does it have to do with the covariance matrix?

I am reading on the bivariate Gaussian copulas and t-copulas.

Copula is just a joint probability distribution. The beauty is that copula models correlation. The downside is it is difficult to formulate different couplas. I like baysian network modelling of joint distributions. Baysian network handles more variables, not only bivariates; the downside is discretization. If you are reading the most recent Significance magazine you will find out all copula can do to the financing industry.

Thank you zlin034. What do you use to simulate copulas, Gaussian and student-t?

I have two ideas for bivariate Gaussian:
1. integrate the density from Wiki, here
http://en.wikipedia.org/wiki/Copula_(probability_theory)#Gaussian_copula

or this,
http://www.vosesoftware.com/ModelRi...n_ModelRisk/Copulas/Vose_Bivariate_Copula.htm

2. use Cholesky-decomposition $\Sigma$=A'A,
then, generate iid standard normal random variables V = (V1, V2)',
then, get Xi from A*V, for i=1,2.
then, get ui= $\Phi$(Xi), for i=1,2.

I am not using R, but even in R there's an algorithm right? Is there a way to see what they did in the package?

R is open source right? Please read the source code from the package

The compressed R packages have file extension .tar, they are called tar balls.

If you open the tar balls, you can see all sources codes are ASCII text files.