What is the best approach to model bespoke CDO skews? There are now several methods to generate skews and deltas on the liquid indices, but what is one supposed to do for a bespoke tranche that has low overlap with the index? What about a CDO of CDO? What if each child CDO has a skew that is different than the other? How to model the parent pool to capture the childrens' skews correctly?

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- I'm not sure 'skew' is standard terminology in this context but I think I know what you mean- I think of skew as a qty which is most relevant when there is a decent two-sided market (i.e. iBoxx)- outside of that universe, you can do whatever you want because there's no liquidity or anything to really calibrate against... i.e. if you're gonna just buy+hold (or sell+forget) then there's little point in thinking any differently than an accountantI mean, you can matrix-price the thing all day long, this will give you a sophisticated drift into the boundary conditions, but without a market mechanism there's no right-or-wrong here. Calibrating against bidlists isn't necessarily a great idea. If you hedge one index with a related one, the resulting distribution is mainly a kind of two-sided Poisson... i.e. no day-to-day "market" moves, but jumps in either direction as mismatched names wipe out. At least from a VaR perspective, you may actually be making things worse.

Fair enough. I was wondering if any factor model was able to explain the skews (let me rephrase this: "correctly price all tranches of the index regardless of their strikes and maturities") of the iBoxx inside (or close enough to be acceptable by RM and controllers) bid-offer, thence be "extendible" to bespoke portfolios. Frankly, although I found it interesting, I view the base correlation debate on the other thread to be kind of a waste of time, because it simply provides a better interpolation method for a market that has a number of observable points, but where do you go from there? In reality, once you have a nice smooth base correlation term structure, and you can do the funky expected loss adjustment for the maturity (the At-the-money thingy), then does that enable you to price a 6.6%-9.2% 3.5y on a bespoke portfolio? On the other hand, if a factor model (with no correlation skews at all, a "real" model) could reprice all index tranches inside bid-offer (i.e. explain the economy) then I would trust that model way more to be extendible to another bespoke portfolio. I guess I'm being idealisitc, but this type of approach was possible in exotic IR derivatives (although that's much easier than our stuff). Related question: What do equity derivatives traders do to mark correlations on their basket trades? isn't each portfolio bespoke in a sense? But maybe there isn't as much tail risk (or high attachement - low equity strike equivalent - hummm EDS does).

QuoteOriginally posted by: j20056What is the best approach to model bespoke CDO skews? There are now several methods to generate skews and deltas on the liquid indices, but what is one supposed to do for a bespoke tranche that has low overlap with the index? What about a CDO of CDO? What if each child CDO has a skew that is different than the other? How to model the parent pool to capture the childrens' skews correctly?1) For a bespoke tranche you would map the expected loss of your bespoke with those of the index and use the equivalent base correlations2) For CDO-squared, it's a mess - I have heard someone calculates skew at the level of each underlying CDO and then at the CDO of CDO level - problem is to figure out how to make the methodology no arbitrageable. Or you can look at a CDO of CDO "equivalent" to a single tranche CDO and take skew out of this equivalent CDO - but you are missing skew at the underlying CDO level plus you come up with a very thin CDO equivalent tranche - for very thin tranches there is some funky behaviour of the skew effect in pricing - so you will have to relax some assumption that will not convince your risk management.

Quote1) For a bespoke tranche you would map the expected loss of your bespoke with those of the index and use the equivalent base correlationsThis seems ok to me, but how would you map the expected losses? It seems there are many ways to do this...How about pricing your bespoke tranche with whichever leaky model and then using indices to check you're not way off?

That's too simple an answer, to check that you're not way off. I guess the real question is "what creates skews"? Is it supply/demand, or is it because of the true dependency structure of a given portfolio. I still think that the latter should be the right answer, and using supply/demand, i.e. index skews for any other lowly overlapping portfolio is just a crap shoot. So answer 1) below seems to assume that the index skew is the right one (once adjusted for the expected loss, a trivial exercise) for a bespoke portfolio. This ignores the true dependency structure of the bespoke portfolio, or approximates it as randomly as any other approach.

not all tranches are created equal, plain and simpleBy dependency structure, I assume you mean that the skew is a function of the underlying asset corr details. I agree, this is undermodelled, but not too many people are able to improve substantially upon this (short of changing the copula function). But tranche structure matters significantly as well, because the risk-management options available to the holder of different notes are quite different. If you hold AAA, you don't bother with the market at all - as soon as the event of default triggers, you pull the plug and flush the collateral... so all you face is either reinvestment risk or structural risk (i.e. you liquidate, but you still didn't cover your assets). If you hold equity, you can at least try to hedge on a single-name basis, or another FTD to hedge corr exposure, etc. Anyhow, the thing really is that capital structure matters. Clientele effects too, don't discount this concept. In a way, that's the genius of CDO - you take a single asset class, and restructure it for different investor classes. It's not all regulatory arb here

Quote1) For a bespoke tranche you would map the expected loss of your bespoke with those of the index and use the equivalent base correlationsThe problem is that the expected loss of your bespoke portfolio is not known. If it were known, you would not need to map anything at all. You would just price your tranche out.If you mean that you take some "prior" CDO model and analyze the modeled expected losses for two portfolios (your bespoke portfolio and some standard one, say, IBOXX); then determine the transformation one need to do to the modeled IBOXX exp loss to match the market exp loss, and apply the same transformation to your bespoke portfolio, then ... well, then there is another problem, namely, your bespoke portfolio could be quite different in properties compared to the standard one (spreads could be different, correlation could be different, maturity too), therefore taking such transformation without an appropriate adjustment will be wrong in general. Whereas to figure, what an "appropriate" adjustment is, by itself is as difficult as the original problem to come up with "right" model.