I had the same reaction as pretty much anyone with a basic background in statistics or simulation had when I saw Felix Salmon's very nice piece in Wired on how mortgage-backed securities and credit-default swaps were modeled: They paid people millions of dollars a year for this utter crap?

As an interesting equation for looking at how you might model prices -- you know, the kind of thing a grad student might do for an exercise or write a thesis on -- Li's work is pretty cool. But as an actual expression of the way the world works, it and its applications were wrong in so many ways it's hard to wrap your head around it. (It reminds me of an old-school video-game programmer, who once explained that you could make at least three different errors in the same line of code: intending to do the wrong thing, implementing that thing incorrectly, and using the wrong syntax.)

As Salmon explains, the equation was wrong for real use because it effectively assumed that the correlations between different securities' prices were fixed, and because it used an entirely inappropriate data set to calculate those correlations. Oh, and because the beliefs about the world that supported the assumption of fixed correlations were at odds with reality. But it was tractable.

At the heart of it all was Li's formula. When you talk to market participants, they use words like beautiful, simple, and, most commonly, tractable. It could be applied anywhere, for anything, and was quickly adopted not only by banks packaging new bonds but also by traders and hedge funds dreaming up complex trades between those bonds.

"The corporate CDO world relied almost exclusively on this copula-based correlation model," says Darrell Duffie, a Stanford University finance professor who served on Moody's Academic Advisory Research Committee. The Gaussian copula soon became such a universally accepted part of the world's financial vocabulary that brokers started quoting prices for bond tranches based on their correlations

In short, everybody buying and selling CDOs and CDSs was living in a dream world, but they were all living in the same dream world, so their results lined up, and as long as housing prices kept rising (preferably at an accelerating rate) their market was internally consistent. If there had been a competing relatively simple formula for pricing these securities, or if people had had the computing power (probably available today on a couple dozen network Playstations) to crunch the behavior of the underlying mortgages or other paper, things might have come out quite differently, but with everybody using essentially the same set of wrong assumptions and biased data,  the market didn't have any huge contradictions.

(About 20 years ago, I gave a talk about the advantage that easily-computable ideas about the world had over hard-to-compute ones, regardless of whether they were right; silly me, I thought the blowup would come in some esoteric application of artificial intelligence.)

So just how far out of sync with reality did the quants' dream world get? From the FT:

From late 2005 to the middle of 2007, around $450bn of CDO of ABS were issued, of which about one third were created from risky mortgage-backed bonds (known as mezzanine CDO of ABS) and much of the rest from safer tranches (high grade CDO of ABS.)

Out of that pile, around $305bn of the CDOs are now in a formal state of default, with the CDOs underwritten by Merrill Lynch accounting for the biggest pile of defaulted assets, followed by UBS and Citi.

The real shocker, though, is what has happened after those defaults. JPMorgan estimates that $102bn of CDOs has already been liquidated. The average recovery rate for super-senior tranches of debt - or the stuff that was supposed to be so ultra safe that it always carried a triple A tag - has been 32 per cent for the high grade CDOs. With mezzanine CDO's, though, recovery rates on those AAA assets have been a mere 5 per cent.

In other words, Holy Crap.

But it's worse than that. It's bad enough that someone would put forward a modeling technique with this level of wrong assumptions and lousy training data. To actually create trillions of dollars worth of securities with pricing based on this known-bad technique took a special kind of greedy stupid, and that same greedy stupid will be right back the next time some mathematician comes up with a crappy-but-computationally-attractive formula.