

Of couples and copulas - geezer
http://www.ft.com/cms/s/2/912d85e8-2d75-11de-9eba-00144feabdc0.html

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ctkrohn
Copula models didn't really work like that in the mortgage-backed securities
world. Mortgages had been packaged into securities for decades before the
copulas became popular, and securities with exposure to prepay correlation
(e.g. CMO sequentials) had been traded since at least the early 80s. For
years, the view had been "mortgage default correlation is hard to model, and
is probably pretty low anyway, so we won't worry about it." A fateful view
indeed.

It wasn't until the creation of the ABX index and then TABX (tranched ABX, an
index designed to mirror subprime CDOs) that people started to worry about
correlation in mortgages. In early 2007, TABX market prices implied vastly
higher levels of correlation than most people expected. That was one of the
early warning signs to investors that their subprime CDOs weren't going to
hold up in a stressed scenario. But almost as soon as those signals were
detected, the market for correlation-dependent mortgage products disappeared.

Gaussian copula models were much more prominent in structured corporate
credit. They became the de facto method of modeling default risk in portfolios
of corporate bonds or credit default swaps. Gaussian copula models, and
succeeding "base correlation" models were necessary to price all kinds of
credit derivatives -- single-tranche CDOs, first-to-default baskets, whatever
you want. Go to <http://www.classiccmp.org/transputer/finengineer/> and take a
look at the Merrill Lynch Credit Derivatives Handbook -- that's probably the
best example of how banks used correlation models in the heyday of structured
credit.

In practice, the Gaussian copula model became the credit derivatives market's
analog of the Black-Scholes option pricing formula. The price of an option
depends heavily on volatility; the Black-Scholes model provides a clean,
mathematically tractable method of extracting the implied volatility from the
price of an option. Once you obtain the implied volatility of several
different options, you can decide which ones look rich or cheap, and you can
use that implied volatility to determine a fair price for other similar
instruments. The model has a number of empirical deficiencies, but
practitioners were able to intuitively correct for them while trading.
Gaussian copulas were the same way. Given the price of two tranches on a
reference portfolio, you could estimate the implied default correlation of the
assets in the portfolio. With that correlation in hand, you can price all
sorts of similar assets. The problem is that copula models are significantly
more complicated than Black-Scholes, and their deficiencies harder to correct
for in practice -- the models had the effect of making traders rather
complacent.

And finally, I hate the trend of bashing quants like David Li and blaming them
for getting us into this mess. The few people that were making an
intellectually serious effort to understand the mechanics behind the market
are not the ones at fault. I think the effort to depict markets as ineffable
black boxes beyond quantitative description is deeply anti-intellectual. The
people most at fault are those who took the quants' research and applied it
uncritically in the pursuit of short term profit, without understanding the
math behind it.

~~~
madair
Agreed.

Looking at the source it's easy to see why this article is a major fail: Wall
Street so desperately wants us to believe that this was all the fault of the
poor people with bad loans they shouldn't have had.

It's pretty funny how they set you all up with all the models and history, and
then tell you at the end, to paraphrase, "but that's all wrong because
obviously all that bad debt should not have been made, and we don't know why
the model didn't work." But we all know that this recession isn't so simple.
What about the overheated market? What about oil? What about hedges? What
about fraud?

Even if we are just taking mortgages to the back shed, take a drive through
upper-middle class suburbs of the wannabe-entitled to see a forest of for sale
signs and foreclosures.

