Hi,Not really a student question, but I've been asked to implement Gaussian Copula to enable us to monitor our CDO exposure. However, I don't have a mathematical background beyond CFA stats, so it's all still very much over my head. Can anyone suggest a reading list in an order that will get me where I need to be without too much distraction?ThanksTom

Check this paper: Understanding the risk of synthetic cdo. It's a good intro to the cdo pricinghttp://www.fdic.gov/bank/analytical/CFR/Septem ... son.pdfYou can also check this website: defaultrisk.com (all you need to know about cdo pricing and even more is there)Finally you can also check the book of Nelsen on copula which is a really great book.

Thanks Meteor - without opening up the docs, do you think that will give me enough bearing in mind that I don't have a PhD in Stats?

to sample from the gaussian copula with correlation matrix R1. Find a decomposition of the desired correlation matrix R such that R = AA' (e.g. the cholesky decomposition, you should now that from cfa, don't you?2. draw n independent standard normal numbers (z1,z2,...,zn)'3. x := z'A4. u := phi(x) , (with phi being the cumulative distribution function of the satandard normal)5. the vector (u1,...,un) is distributed according to the gaussian copula with desired correlation matrix R.

QuoteOriginally posted by: MrHappyThanks Meteor - without opening up the docs, do you think that will give me enough bearing in mind that I don't have a PhD in Stats?I guess you will have to open the document to see if you can understand them. But the Gibson paper definitely worth a look. I would say it's the easiest explaination of the cdo pricing with factor copula I've seen so far.

Hello, I am looking to implement a generic copula solution for future modelling efforts. I am looking to extract commonality between the elliptical and archimedean copulas. Secondly, I am trying to determine the separate responsibilities needed for handling of theseobjects (ie Simulation, Calibration, Analytic Representations of the Distributions).The first thing I would like to do is to tackle calibration. What are the basic concerns, here? For archimedean copulas, it seems to me that you calibrate to find your theta parameter. For example, consider that I have a time series for each of 3 random variableswhere the marginals are (1 Gaussian, 1 Gamma Distributed, 1 T-Distributed), I translate each of these to their grades U(0,1) via the CDF. Then I optimize the log-likelihood problem to find the theta (input to the archimedean copula) that best fits (smallest normed distance) over all the points in the time series. Am I missing something?Thanks In Advance.

MATLAB implementation of the Student's t copula can be found at http://www.ee.iitb.ac.in/uma/~saket/dat ... htmlThanks.

MrHappy,I'd just like to point out that genkideska's comments refer to the Monte-Carlo based for pricing a synthetic CDO and not specifically to the Gaussian Copula itself. Just so that you understand, the purpose of the copula is to compute correlated default probabilities for each entity in the CDO from the individual default probabilities. After that, the loss distribution for the portfolio needs to be built and this can be done by either simulation or an (semi-)analytical method.The Gibson paper discusses the latter using the Gaussian copula.

Do you have to implement the gaussian copula yourself? Otherwise there is an open source statistical software package called R that has an implementation for the Gaussian, t and certain Archimedean copulas. This library is relatively easy to use. If R isn’t installed, download R from http://www.r-project.org/. When R is installed - install the copula library (Package -> install packages -> copula.zip) and then load the library. Often you are not interested in the copula itself but rather a probability distribution which implicitly has a certain copula dependence structure. When you have specified a dependence structure along with marginal distributions you have actual constructed a multivariate distribution function. In R you can simulate from this distribution but you also have access to the probability and density function.#R-codelibrary(copula)#Construction of the multivariate probability function with a gaussian copula (correlation = 0.3). The marginal distributions are a beta(5; 200) and a log-normal(-4; 0.5).thisCopula <- normalCopula(0.3, dim = 2, corstr = "un")this.mvdc <- mvdc(thisCopula, c("beta", "lnorm"), list(list(shape1 = 5, shape2 = 200), list(meanlog = -4, sdlog = 0.50)))#10 Random draws from the probability distribution with a Gaussian dependence structure. rmvdc(this.mvdc, 10) #Probability: P(marginal.1 < 0.05; marginal.2 < 0.09) pmvdc(this.mvdc, c(0.05,0.09)) #Density: dmvdc(this.mvdc, c(0.05,0.09)) #End R-codeHope this helps/Jonas

Thanks, I have referenced the R implementation and have modelled the interface from that interface. My applications will be for CDO's, equity basket options, and prepayment factors for MBS. Does anyone know of a good reference that shows general (for any n) derivations of the PDF's of the Clayton, Gumbel, and Frank copulas? I have been able to derive the Clayton copula pdf but I am having difficulty deriving a general expression for the Gumbel copula. Can anyone help?