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What is copulas exactly, in probability and finance terms

  1. Mar 15, 2012 #1
    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.
     
  2. jcsd
  3. Mar 15, 2012 #2
    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.
     
  4. Mar 15, 2012 #3
    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 [itex]\Sigma[/itex]=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= [itex]\Phi[/itex](Xi), for i=1,2.
     
  5. Mar 16, 2012 #4
  6. Mar 16, 2012 #5
    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?
     
  7. Mar 18, 2012 #6
    R is open source right? Please read the source code from the package
     
  8. Mar 18, 2012 #7
    Last edited: Mar 19, 2012
  9. Mar 19, 2012 #8
    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.
     
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