Whew!!! A real flurry of replies this weekend...I'm going to try not to get too much involved in a "my method's better than yours". It looked like this was turning into a little argument over the weekend (we almost had some name calling with the "third tier" stuff), but as I published here to try to get a discussion going, I can't really complain. (But as almost everyone else except me is anonymous, I'll have to keep myself in check.)I guess I have to make a couple of points. Approximately in order of first posted:CreditGuy: In answer to your old question (and perhaps the reason why nobody answered) is on first reading it looks like "why not just use history or theoretical" (hence the reply about risk neutral, hedging costs), but it seems that your actual question is "how do you value tranches of non-standard portfolios"? I'd love to have a discussion about this, it's what we are working on at the moment. As always there are no right answers though.Complexity: "wrong" concept seems very harsh. If there were any right or wrong answers in this world or correlation, then there would be no room for discussions... For what it's worth, I think your analogy is off - the analogies that work and that drive our thinking are options based. Base correlation is like calulating one implied volatility per option rather than one volatility per option spread. When you talk about calculating your hedges, I think the main point is that you have to be consistent - you cannot get a Base Correlation number from one model and use it in another framework. Or vice versa. Moreover, "Correlation smile" is absolutely meaningless in the context of compound correlations from gaussian copulas (having said there are no rights and wrongs, perhaps that's inflamatory), unless someone comes up with a new model where a smile is the outcome, and I can't see the point of that. Whilst you might be able to argue that a compound correlation is well defined for a specific tranche, there is no meaning to joining up the lines, which is what turns dots into smile. (Next research note on this real soon, but the multiple solutions have a much worse impact than we previously thought.)As to whether Base Correlation is enough, or a better model (which correctly models the market observed prices, giving a single correlation) is possible. I would argue the following:1. "Correlation" is only interesting if it changes, and changes relatively across the capital structure. That is if historical correlation tells you all you need to know about pricing, then there is no use or interest calculating either a Base or Compound Correlation.2. Even if you could find a model which worked well for current tranche spreads (and gave you the same single correlation number for each tranche), then as soon as there was a mismatch in supply and demand across the captial structure (or any one of a number of other market metrics), then a skew/smile is likely to appear. If you can't get rid of it, better to understand why it is there, in my view. (Alternatively, you may find that one of your other parameters is changing, but that's equivalent, I think.)In terms of whether Base Correlation is useful. I will argue strongly that it is much more useful that compound correlation using a gaussian copula. Because of the propensity for skew to always exist, I think it important to standardise on a model to discuss it, rather than try to get rid of it. I'm happy to discuss other models, but even a gaussian copula hasn't been practical for making the market more transparent to clients. If clients cannot reproduce what the banks do, then any quoted correlation numbers may as well be random. New models are likely to be harder to implement and calibrate, I would suggest.I wouldn't argue that the use of Base Correlation replaces other means of pricing and hedging etc. Like in equity options, just because everyone uses Black Scholes externally, doesn't prevent you having a more sophisticated internal model.Phew! Sorry if that's too much in one mail. And sorry if I've spoken out of turn. I'm appreciating the discussion.RegardsLee

QuoteOriginally posted by: leemcgComplexity: "wrong" concept seems very harsh. If there were any right or wrong answers in this world or correlation, then there would be no room for discussions...Sorry, if I've upset you. I take the "wrong concept" back. But as you can see, strong controversy can further discussion. I just try to disagree, whenever I can

Don't worry, I'm not upset, but as the only person around who's not anonymous (it seems) and one who is clearly associated with a particular firm, the last thing I want to happen is to get involved in a very public slanging match. I know how this things can deteriorate!RegardsLee

Any one has comments on leverage impact between base and compound correlations? I find that the leverage factors between both methods are widely different (9x versus 13x) although they both reprice at the same PV. The derivatives are really different.

It's not the Base Correlation framework that can give you deltas, rather the Large Pool Model.That said, the deltas it gives are "correct", or intenally consistent as it is a calibration model.That doesn't mean that this is the best or most efficient delta by any means however.On the subject of deltas though, I would say that there isn't general agreement on the values of deltas or how to calculate them - I hear rumours that one dealer was quoting deltas on the 3-6% tranche higher than the 0-3% tranche yesterday!So to answer your question, you can only compare deltas if you can be calculating them yourself with all of the same inputs and in that case, I'm not sure in what way Base/Compound correlation can make any difference. (Thinks a bit)...Unless you mean that with the same LP model and same assumptions (0% discount, 40% recovery), that if you hold Base Correlations constant or Compound Correlations constant (or ATM Base Correlations constant) that you have very different deltas. This is interesting, and opens up many questions about what is best...RegardsLee

The latter indeed. Keep all correlations constant, no ATM/OTM adjustment, then bump spreads by an 01. Ignore LP model, straight gaussian copula or 1-factor central shock model. Curious.

Well that is very interesting... The issue then is what does it mean to keep correlation constant... I think it's particularly misleading to keep 3-6% compound correlation constant because its an artificial construct. (More on just how artificial this is soon). But it is likely also wrong to keep 3% Base Correlation constant - because as you change spreads what 3% means changes as the expected loss changes...If you're in a simple world where you have models and you use historical correlations, there is no issue, but once correlation becomes an observable, it gets much more interesting.One interesting question, on the tranches where you have more than one solution for compound correlation, do you get massively different solutions for delat if you keep correlation the same as the upper or the lower solution. If you do what would that mean for the deltas you get? (My guess: that deltas derived from compound correlations are not very useful, but I don't know what the numbers look like).RegardsLee[small edit for missing word]

I think we need a definition of what we understand by delta. I can think about a number of possibilities:a) Take the (weighted) average of single name bump/analytic deltas holding base correlation constant. I.e. average of partials w.r.t. spread.b) Compute index delta by shifting index level, keeping base correlation constant.c) Compute index delta using fixed compound correlation.d) First, shift the index level to derive new expected loss. Anchor the original base correlation curve at "new" expected loss. I.e. move the skew curve s.t. ATM correlation is the same after and before the shift. Second, proceed as in a) or b).e) etc.for a), b), and d) there would be two first loss tranche delta computations for each ith loss tranche, i > 1.All of these also work for single name delta calculation.

Good way of putting it Complexity. I might just add the following at the beginning...There is an intuitive definition of delta, that is how much does the instrument price change, when the underlying market changes by 1bp, if nothing else changes.The issue when defining delta then becomes twofold: 1. What do we mean by the underlying market moving by 1bp, and 2. what do we mean by "nothing else changes" - particularly in terms of correlation?Depending on our answers these questions, this leads to many possible definitions of delta...(then I'd continue with your reply, some of which refer to what does an underlying spread move mean and some about what does keeping (correlation) constant mean)As to my view on the answer, there are two parts...1. What does 1bp mean?This should mean the index changing (which can happen without the underlying spreads changing at all), although it would be a real surprise if single names (once adjusted for basis to theoretical) moving by same % of spread, or by bp would give any difference.2. What does keeping correlation same mean.For this, you should use whatever you think is the right/best method to measure correlation. That is the only way you get consisent measures. For example, tomorrow, the ATM Base Correlation and skew could stay the same, but Base Correlation by attachement and compound correlation would likely change. I think that it's going to become harder to justify that compound correlation is the right thing to do, and from that premise it becomes clear that compound correlation staying the same doesn't have an measing that very close to intuition. But I am of course, biased!Such a delta definition will not stop people looking for the best and most efficient hedge ratio for their own use, however.RegardsLee

On your last point, I would agree that any of these deltas are not risk-neutral hedges, but rather hedging strategies. It's not clear ultimately which delta is right, although you almost have to take a statistical hedging view of the world to answer that.Anyways, if we stick to the definition of 1bp shift in all CDS instruments (which should be close to a 1bp shift in the index), and NOTHING ELSE CHANGES, regardless of the correlation framework, then I got back to my question that a compound correlation versus a base correlation calibrated to the same tranche yields different leverages (i.e. the first order dP/dSpread derivative is different by as much as 40% relative). Just curious what the insight is.

The only insight I can give is that compound correlation not changing is very different to Base Correlation not changing (which is different to ATM Base Correlation and skew not changing). Then we have to choose which is "best".RegardsLee

j20056, approx. what compound correlation and what base correlation are you using?

I notice that Bear Stearns has done an interesting piece on the different deltas - they get similar results to you.Main conclusion (to paraphrase - apologies if any Bear people are reading) is that deltas are very different, Base Correlation deltas have been historically "better" (I think this is a function of Base Correlations not moving as much in the history used) but given that we don't really understand how correlation moves, it is too early to say what is the best delta.I obviously can't go giving out someone else's research so please don't ask :-)RegardsLee

QuoteOriginally posted by: leemcgI notice that Bear Stearns has done an interesting piece on the different deltas - they get similar results to you.Well, my friend, because you posted lots of articles and excel spreadsheet, it would be nice and fair to get also other firms' stuff...

QuoteOriginally posted by: CreditGuyWell, my friend, because you posted lots of articles and excel spreadsheet, it would be nice and fair to get also other firms' stuff...I'm starting to develop a serious dislike for you "CreditGuy"...