# [R-SIG-Finance] Elliptical Copula simulation

Xiaochen Sun Xiaochen.Sun at brunel.ac.uk
Wed Apr 1 12:06:33 CEST 2009

```Hi there,

If I understand right you want to calibrate (fit) normal/t copula with the given data set, right? Then you can do whatever you want, such as simulate random samples from the fitted copula functions.

Firstly, I think the package {QRMlib} is more preferable. You can estimate the two copulas by using functions "fit.gausscopula" and "fit.tcopula". (And of course, you can also fit Archimedean Copulas with relevant functions, but limited to 2 dimensions.)
The input data here must be pseudo-copula data, which means you have transform your original data into uniform data. This could be done either by using empirical distribution function (CML method) or fit it with certain distribution family (IFM method).

Secondly, in terms of nonparametric estimation you can find relationship between spearman's rho/kendall's tau and copulas. For example, the relationship between elliptical copula and kendall's tau is give, tau = 2/pi arc sin rho.

Lastly, there are some good references on this topic, for example
[1] Book, "Quantitative Risk Management: concepts, Techniques, and Tools" by McNeil, A.J., Frey, R. and Embrechts, P.
[2] Paper, "Kendall's tau for elliptical distributions" by Lindskog, F. McNeil, A.J. and Schmock, U.

Hope this helps.

Cheers
Michael
P.S the example you listed below is to construct a copula object with known copula parameters, distribution family.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Michael(Xiaochen) Sun, BA(BTBU), MSc(Hull), PhD Student,
CARISMA, www.carisma.brunel.ac.uk <http://www.carisma.brunel.ac.uk/>
The Centre for the Analysis of Risk and OptimISation Modelling Applications
School of Information Systems, Computing and Mathematics
Brunel University, Uxbridge, UB8 3PH, Middlesex, United Kingdom
Telephone: +44 1895 265625 [M503], Fax: +44 1895 269732
Webpage:http://people.brunel.ac.uk/~mapgxcs <http://people.brunel.ac.uk/~mapgxcs>
http://ssrn.com/author=974259 <http://ssrn.com/author=974259>
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

________________________________

From: r-sig-finance-bounces at stat.math.ethz.ch on behalf of tawfiq just
Sent: Wed 01/04/2009 09:22
To: R-SIG-Finance at stat.math.ethz.ch
Subject: [R-SIG-Finance] Elliptical Copula simulation

hi everyone
I have  a multivariate time series let say a 3*50 matrix dimension. the
correlation matrix is

1            0.22      0.25
0.22       1          0.43
0.25       0.43        1

i would like to simulate both normal and student copulas, from the help in R
they didn't explain how to use the correlation matrix or to evaluate the
degre of freedom to fit the copula for the student copula estimation.

Examples and copula functions in the copula packadge document
ftp://ftp.auckland.ac.nz/pub/software/CRAN/doc/packages/copula.pdf

norm.cop <- normalCopula(c(0.5, 0.6, 0.7), dim = 3, dispstr = "un")
t.cop <- tCopula(c(0.5, 0.3), dim = 3, dispstr = "toep", df = 2)
## from the wrapper
norm.cop <- ellipCopula("normal", param = c(0.5, 0.6, 0.7),
dim = 3, dispstr = "un")

*Fit a copula model to multivariate data.*
Usage
loglikCopula(param, x, copula)
loglikMvdc(param, x, mvdc)
fitCopula(data, copula, start, optim.control = list(NULL), method = "BFGS")
fitMvdc(data, mvdc, start, optim.control = list(NULL), method = "BFGS")

any help please on this topic.

think you very much

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