Hi,I'm interested in implementing the gaussian copula method to price first to default contracts. Typically would be on sovereign issuers (5 or 6).I already understood how to generate random numbers with a Normal correlation structure with the use of the cholesky decomposition.But I can’t understand how to obtain the time to default. I can obtain it by doing F-1(u), but I can’t figure out how to choose the Marginal distributions. I read somewhere that the usual is to consider an exponential distribution of the survival time.How can I estimate the hazard rate and the correlation matrix? What other marginal distributions could I use? How can I estimate the parameters and? As you can see I’m really confused. Any help would be much appreciated.Any good book for starters like myself (maybe with some numerical examples)?Thanks in advance,Pedro Raquel

Regarding the estimation of marginal distributions you could try nonparametric estimation, which will use empricial CDF or Kernel Estimation. If you fix the type of distribution you could use MLE to estimate the parameters. Most common distributions are GEV, GPD distribution.As to implementing, S+ and R had some good package!(R is free)Relevant Book:Copula Method in Finance

But what data should my distribution fit? Should I use the default probabilities? Survival probabilities???Could you be a little more specific pls?Thanks