BTW, some of us are still eagerly awaiting part III.

Which reminds me... I wonder if in part III you could address the issue of static recovery assumptions. This is more than the issue that market recovery inputs are difficult to observe (absent transparency into fair spreads for fixed- or zero-recovery swaps). Even if you have such data, it seems a problem--particularly in the pricing of senior tranches--that the standard SFGC model ignores recovery dynamics. The simplest illustration of this problem is a super-senior 60-100 tranche where all recovery rates are 40%. No correlation level will allocate losses to this tranche, since even if all reference credits default simultaneously, this tranche will walk away with their full principal.

I believe there are a few papers out there that describe proposed extensions to the SFGC model to introduce dynamic recovery. I'm not that familiar with these methods, so if someone could deconstruct them, that'd be rad.

"A CDO is nothing more than a collection of various bonds... Both the timing and the correlation of defaults matter... This issue is compounded by the introduction of tranches."

Tranching does not COMPOUND the issue, it IS the issue. Correlation does not matter until you introduce tranching. If you have a 0-100 "CDO", which is the simple case you describe of holding a basket of bonds (or CDS if synthetic) sans tranching, that is identical to holding the same bonds (CDS) individually, with no basket to hold them.

So, it's not that the *first* mine is more or less likely to be hit, it's that conditional on missing the first mine, the others are subsequently less likely to be hit.

For an example, consider a CDO made up of 100 banks. This is high correlation - they're either all defaulting, or all surviving. You want to own the equity here because if they all survive, which is a distinct possibility, you will get a huge payoff. But if you have a diversified portfolio, its less conceivable that every name will survive (since there is more idiosyncratic risk), and since there are less "clear paths across the bathtub", you would rather have a stronger tranche.

Is this actually true for CDOs in real life? The implication would be that the odds of any single (first) default are lower for a highly-correlated basket than for a diversified one.

Why and how would this be the case?

Think of a freeway with random cars traveling along it (the "mines"). Add another car (the "boat") trying to pass through at high speed --- a police chase, or a video game like SpyHunter.

Then as above, if the cars are fairly evenly dispersed (low correlation), a collision with one is unlikely to result in a second collision. But if the cars are traveling in clusters (high correlation), one collision will most likely cause a multi-car pileup.

And if the "boat" car is a lightweight sports car, a single collision will wipe it out (equity investors). But if it's a Hummer or Range Rover, it might handle several collisions (senior investors) and therefore prefers low correlation.

Just thought this might be helpful! (NB: I'm a humanities grad student, not a finance guy, but I've done a lot of reading and think I understand this...)

Performativity always wins in the end.

I'm excited for part III.