# What is copulas exactly, in probability and finance terms

1. Mar 15, 2012

### colstat

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.

2. Mar 15, 2012

### 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.

3. Mar 15, 2012

### 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 Xi from A*V, for i=1,2.
then, get ui= $\Phi$(Xi), for i=1,2.

4. Mar 16, 2012

### zli034

5. Mar 16, 2012

### 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?

6. Mar 18, 2012

### zli034

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

7. Mar 18, 2012

### kulimer

Last edited: Mar 19, 2012
8. Mar 19, 2012

### 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.