What is copulas exactly, in probability and finance terms

[colstat]

Hi, all
I have been reading about copula, but still very confused.

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.

 

[zli034]

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.

 

[colstat]

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 X_i from A*V, for i=1,2.
then, get u_i= $\Phi$(X_i), for i=1,2.

 

[zli034]

You can look at R package
http://cran.r-project.org/web/packages/copula/index.html

 

[colstat]

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?

 

[zli034]

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

 

[kulimer]

Do you know how to read the source code? Yes, it is open source, but how do you actually see it? Say, the copula package for example.
http://cran.r-project.org/web/packages/copula/index.html

 

[zli034]

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.