Does someone have some experience with synthetic CDOs and their quotes on Bloomberg?Using the standard market model (gaussian copula), if I use the base correlation quotes I can't match the prices of the tranches.For example, in the case of the current iTraxx series (S24) 5Y, I see the following quotes for the equity tranche (0% - 3%) Index spread: 80 bpsUpfront 44.692 %Base correlation 56.802 %and the tranche is running under fixed spread 100 bps.Using the gaussian copula model and the base correlation above, I got a breakeven upfront about 36 %.I have done the same exercise with CDX NA too but with a similar result (inconsistency).The model is giving me good results when benchmarked against Hull's data and his results.So, where might be the problem?

Try running the BBG CDST function. That should match the quotes and related base correlations from CDOT. Key word being *should*...

I tried CDST and it seems to produce results consistent with the quotes. I asked the helpdesk for some documentation about how their model works and I was told their methodology is based on Bjorn Flesaker's paper: Fast Solution of the Gaussian Copula Model. I have the paper: paper but it does not seem to me that it includes all the necessary info.If anyone were interested in solve this "puzzle", I would appreciate the cooperation.

The implementation details are unlikely to be terribly important as long as you respect the spread dispersion in the underlying portfolio. Your reference to "the gaussian copula model" evidently is to an approximation that relies on a homogeneous spread assumption. That will produce the sort of error you find, and is not particularly useful with the current index compositions. In fact, it is considerably worse for CDX IG, which has even more junky energy and metals & mining names.

What do you mean by the "spread dispersion"? Do you mean the relative variability (or non-homogeneity) in CDS spreads of the credits in the basket? I don't think this should be a problem. If I'm not wrong, the index quote is not a simple average of the CDS spread of the credits in the basket but its composition is slightly more complicated, also reflecting the variability to which you are probably referring to. Through the index quote, I think this variability is also incorporated in the tranche quote.So, what do you think is a correct approach? To calculate the loss distribution according to CDS (and the implied default intensity) of every CDS quote in the basket instead of using the pseudo "average" index spread?Thanks!

Consider an index portfolio with 7 names that each have a flat 5Y spread of 1,000 bps and 118 names with corresponding spreads of 40 bps. The fair index spread will be around 78 bps if we assume a 40% recovery rate (the average spread is about 94, but that's not relevant). Consider another portfolio where all names have spreads of 78 bps. If you are willing to provide me protection on a 0-3% equity tranche in the first portfolio in exchange for my providing you the same protection on the second portfolio, we have a deal!

I agree with what you say and now a question appears in my mind: if an implied correlation is quoted for a tranche, does this correlation apply to (i) a model in which all the credits are assumed to be equal, or (ii) to a model in which the credits are allowed to be different in terms of the CDS-implied default probabilities?If I imagine the case (i), then in your example the quoted implied correlations on the equity tranche of the first and second portfolio won't be equal to provide different prices for the equity tranches while the spread is assumed to be 78 bps for all credits in both portfolios.In the case (ii) the correlations could freely be equal because if in the pricing model each credit is allowed to retain its CDS-implied probability of default, then this will automatically result in different prices of the equity tranches in each portfolio. But what justification would have index quote (iTraxx, CDX NA) then?The thing is that (i) is what the benchmark literature is usually referring to, particularly in connection with Vasicek's LHP approximation. The case (ii) seems, however, much more credit-sensitive and personally for me makes more sense.My question is: shall the implied correlation be used in the approach (i) or the approach (ii)?

I have done a small exercise - I downloaded CDS quotes for all the names in the basket (both iTraxx and CDX) and computed the fair upfront on the equity tranche by allowing every name to retain its default probability implied by its CDS, with the implied correlations for the equity tranche. This corresponds to the model (ii) that I mentioned below. The results are, however, still not matching the Bloomberg quotes. For iTraxx (0-3%) I haveupfront: 29.44 % (quoted upfront is 43.75 %)For CDX (0-3%) I haveupfront: 46.90 % (quoted upfront is 62.50 %)Where could be hidden the clue to this?