I'm trying to mimic the methodology and results of David Li's paper on Default Correlations a Copula Function approach.If my understanding is correct 1) first simulate n random variables Y1...Yn from a multivariate normal with correlation matrix R.2) Map back the Y's to to ti's the default time of the ith issuer. using tj = Fj^(-1)[N(Yj)]with Fj being the cdf of an exponential distribution with parameter h ie. F(x)= 1- e^(-hx).Then the default time tj = -1/h ln (1- N(Yj))is h obtainable from the CDS spread ie. h = CDS Spread /(1-Recovery rate)?I guess my questions are -how do you find h for different issuers if the term structure of CDS quotes is not flat.Secondly, does anyone have code, to perform the cholesky decomposition for the correlation matrix R - (or better still code to simulate the correlated defaults of n issuers ?)I'd also appreciate any information if i've said anything incorrectly, or misunderstood the methodology.thanks apologies for not being able to get the subscript notation in here. this was my message didn't go through on the original post thanks.

you can only use h=s/(1-R) if you assume a flat term structure of spreads. This is a very common assumption and should give you reasonable prices, certainly for quoting (use the appropriate maturity for the basket). The Riskmetrics technical paper on VaR has a routine for cholesky (couple of typos) and numerical recipes has several routines that are of use (doesn't have to be cholesky)

if you want the code for the cholesky decomposition have a look in wilmott's "quantitative finance" part 2 (vba code) or glassermans "monte carlo methods in financial engineering" (pseudo-code). i typed in R id you are interested i can sent it to you.

Hi babolat,For 2) Map back the Y's to to ti's the default time of the ith issuer. using tj = Fj^(-1)[N(Yj)]with Fj being the cdf of an exponential distribution with parameter h ie. F(x)= 1- e^(-hx).Then the default time tj = -1/h ln (1- N(Yj))Doubts:1) Are u assuming that the hazard rate is constant throughout the life of CDS?2) What IF the hazard rate is not constant throughout and is constant only during certain periods of the life? Then F(x) is expressed in another way ?...... F(x) = 1 - exp( Summation (h(i)*x)) -Correct me if i'm wrong.....In such a case, how do we define the default time tj ?3) For: tj = Fj^(-1)[N(Yj)] If hazard rate is not constant, how do we calculate Fj^(-1) ?