How can PFE be calculated for CDO tranches

[spiffy]

Can anyone here advise on how to calculate potential future exposure for CDO tranches?



Thanks.

[sfca]

I'm rather sure I'll regret suggesting this, and I haven't really thought about it.  And the answer depends on what you personally want out of this (yes, really).  Anyway, how about using the standard gaussian one factor model (eg. Factor Models for Synthetic CDO Valuation by Merrill or the Portfolio Modeling Handbook by CSFB) and plugging in the worst case loss at future points as the systematic factor (note it enters the expression as the inverse showing how many standard deviations produces that worst case loss) generated from something like the Moodys tables of losses over time.  This gives the tranche spreads (after some fun with guassian integration) and then compare those to the original for the mtm.  You'd obviously have to modify it a little because over time the spread on the potentially declining notional would fall as the notional falls, but thats hopefully dealt with as a detail.  This seems too simple so theres probably something wrong with this, beyond the obvious.  The obvious being the gaussian assumption has little to do with actual credit distributions, but because its easy to apply is very common.  But the auditors will love it.  And, if you are familiar with the math and stats, you literally could have this PFE model running today.  If you want greater accuracy, the more complicated copula models are mostly worth pursuing only if you want to sharpen up your statistics skills.  If you want a more realistic answer, actually if I were asked to do this, I might start with a monte carlo simulation of the defaults and loss severity (they are highly correlated) with statistical distributions representing historically estimated dispersion but with economics determining the central tendency and adding a second factor representing sector risk (remember those nasty auto issues a few years ago?).  Then, I'd take those results to see if they could be stuffed into a quicker semi-analytical expression like the earlier model somehow.  Anyway, as I said I am writing this without really thinking about it and will probably regret all of what I've said later.

[sfca]

In the future you might want to at least acknowledge one answer here before you start posting this same question on other sites.  It kind of kills my interest in helping any more.

[Cheng]

There is a lot to say here but I am not sure whether it should be said.

[spiffy]

Cheng,



You tease. If you were to decide things should be said then I'd be glad to listen.

Or if you could point me in the direction of places where this stuff has been written about (book, online, whatever) I'll go and read it.



 



sfca,



Thanks for your ideas.

I posted the question simultaneously here and the other place because I'd been led to believe the intersection of the readerships is small (with NP being a higher-quality, less well-known site).

[Cheng]

Mkay,



if you are serious search the phorum. Some people, including myself, said a lot about credit related stuff.



Two hints: think Bayes and look for dynamic models.