Hull&White CDO pricing via a structual approach and a confused student

Maggette · Post by **Maggette** » Mon Jul 23, 2007 10:21 am

Hey guys, first things first...I am an MBA student, so please don't kill me for a stupid question Blush

I recently ran into thishttp://www.rotman.utoronto.ca/%7Ehull/DownloadablePublications/StructuralModel.pdf

After the first moment raving about how nice and cute he is modelling the default correlation via an structual approach, I am confused now..what's the point of the model? At the end of the day, he(Hull) is comparing market prices vs the prices implied by his monte carlo simulation..I think that these spreads are results of trading in the market(obviously)..so what's the point of replicating prices I allready know? Since these standard tranches(CDX,itraxx) are heaviely traded I have to take the quoted spreads as a matter of fact. He is pricing via a monte carlo simulation and not by dublication..so if his model states a different ''better" price than the market price, he has no hedging portfolio to cash in arbitrage and enforce the "right" spread....the only application of the model I can think of is to use it for calibration of the default correlations of the different assets and use these correlations for other less traded products involving the same assets..so again, what do I need this model for? ..Sorry again, if I am wasting your time by asking something stupid( since Hull & White are smart, it is obvious that I am missing something)

IAmEric · Post by **IAmEric** » Mon Jul 23, 2007 1:13 pm

I'll take a stab and in the usual tradition, will probably be wrong, but hope that someone who actually knows can come in and save us...

It is not so much about reproducing market prices that is important, rather it is what information the model allows you to extract from market prices. In the case of bond prices, you can extract "yield", which if you think about is a pretty hollow number, but it has merit in the sense that it aids the comparison of different bonds. In the case of vanilla options, you can extract "implied vol" which is morally not so unlike "yield" in the sense that it is similarly hollow, but allows you compare relative value. I haven't looked at the Hull paper, but I could guess that the important thing to extract from the prices is probably "implied corr" or whatever you call it. This will (they hope) help you compare CDO for relative value.

Ok. Now that the amateur has spoken, I'll move aside for the experts Smiley

Cheng · Post by **Cheng** » Mon Jul 23, 2007 1:58 pm

I just skimmed through the paper and it rings some bells (structural multi-step model vs default time copula vs reduced form model, stochastic correlation, etc). Let me read it in full detail, I will be back. But if you are not familiar with credit this might become a bit too technical Wink .

Maggette · Post by **Maggette** » Mon Jul 23, 2007 3:58 pm

The technical side is not really a problem...I visited Phd classes on time continuos finance theory, so I can reproduce the equations and the other mathematical stuff he is using in this paper(I am not as good as physic/math/statistic students, but I have heard of PDEs,SDEs and Itos lemma..not that I really undrestood and mastered anything of that stuff but the paper doesn't use anything too fancy, if I did not miss anything) ...like I said, the problem I have is more on the practical applications of the model. Is there anything I can do with the model, besides using it as calibtration tool to get default correlations [img]/User%20Files/3110/MathML-Equation-6660.gif[/img](which is, in my opinion, a computational disaster, because you should (again my opinion) treat the default correlation like an implied vola and do it over and over again (so I don't think the default correlation is a time independent constant)..) Like IAmEric posted, maybe you can use it to back out the implied default correlations..but the best fit of the models appears when the alpha factors are a random variable ..so I could use the model to calibrate the parameters of a beta distribution to model my "implied stochastic default correlation"? To me that sounds like BS(thats Bull Shit and not Black Scholes) Confused But again..I am not the sharpest or fastest guy in the world Smiley

Cheng · Post by **Cheng** » Mon Jul 23, 2007 4:57 pm

Ok, I quickly read it. So far there is not much new except for the multi-step approach (you don't do one time step and check whether you defaulted but several). This makes more sense and might yield better time dynamics (Gaussian copula is a bitch here) but the parameter problem remains. The Gaussian coupla model does not fit observed market prices (aka correlation smile/skew) which is why people came up with base correlation.

Trying to estimate pairwise default correlation from market prices is impossible (at least a major mess) and doesn't help anything since the model doesn't explain market prices properly. Stochastic correlation was proposed as a remedy but I doubt that it really works.

One point that is also interesting is that the authors use market data from Aug 2004. The market has changed since then and I doubt that they would get similar results using current data.

HTH.

Maggette · Post by **Maggette** » Mon Jul 23, 2007 5:03 pm

Thanks for the help Cheng..saved my day..

Maggette · Post by **Maggette** » Thu Jul 26, 2007 9:25 am

Hey Cheng, after your reply I tryed to figure out what you tryed to say with"The market has changed since then and I doubt that they would get similar results using current data"..after thinking about it for a while I have to admit: I don't get it(besides the trivial stuff..the market has changed? of course..threfore not getting exactly the same results is obvious..but I think you thought of some more general problems..like you can't use that approach at all, because of certain changes in the market) can you give a short explanation or maybe a hint or a link so I can figure it out by myself

Cheng · Post by **Cheng** » Thu Jul 26, 2007 9:57 am

My impression is that the market has changed fundamentally after the May 2005 sell-off. People employ different strategies, the once famous Long Equity/Short Junior Mezz trade for example disappeared. Equity tranches also behave differently due to new products like equity POs and principal protected (rated) equity.

Take for example Hull+White's double-t copula model (you should find it on defaultrisk.com). By the time the paper was published they could reproduce market prices but now the model does not fit the market anymore. This is what I mean when I say the market has changed. Synthetic structured credit is extremely technically driven and this is reflected in the models.

Maggette · Post by **Maggette** » Fri Jul 27, 2007 11:04 am

Thanks again, Cheng.. ...so it seems the model has not really any practical application...too bad..I really thought about playing around a little bit and trying to extend it..now I can throw the Matlab code away....that equity PO stuff sounds interesting Smiley

Cheng · Post by **Cheng** » Fri Jul 27, 2007 1:05 pm

Well, I think the multi-step approach has its merits and is better than the usual copula thingy. But there have been other models utilizing the same idea without the drawbacks.