http://www.wired.com/techbiz/it/magazine/17-03/wp_quant?currentPage=1

This article analyzes how David X Li’s work caused the worst economic meltdown since the Great Depression. Its opening paragraphs set the stage:

“A year ago, it was hardly unthinkable that a math wizard like David X. Li might someday earn a Nobel Prize. After all, financial economists—even Wall Street quants—have received the Nobel in economics before, and Li’s work on measuring risk has had more impact, more quickly, than previous Nobel Prize-winning contributions to the field. Today, though, as dazed bankers, politicians, regulators, and investors survey the wreckage of the biggest financial meltdown since the Great Depression, Li is probably thankful he still has a job in finance at all. Not that his achievement should be dismissed. He took a notoriously tough nut—determining correlation, or how seemingly disparate events are related—and cracked it wide open with a simple and elegant mathematical formula, one that would become ubiquitous in finance worldwide.”

“For five years, Li’s formula, known as a Gaussian copula function, looked like an unambiguously positive breakthrough, a piece of financial technology that allowed hugely complex risks to be modeled with more ease and accuracy than ever before. With his brilliant spark of mathematical legerdemain, Li made it possible for traders to sell vast quantities of new securities, expanding financial markets to unimaginable levels.”

“His method was adopted by everybody from bond investors and Wall Street banks to ratings agencies and regulators. And it became so deeply entrenched—and was making people so much money—that warnings about its limitations were largely ignored.”

“Then the model fell apart. Cracks started appearing early on, when financial markets began behaving in ways that users of Li’s formula hadn’t expected. The cracks became full-fledged canyons in 2008—when ruptures in the financial system’s foundation swallowed up trillions of dollars and put the survival of the global banking system in serious peril.”

There are significant similarities between Li’s work and the GCMs that the AGWers, media and policy makers ignore at their peril. If they get their, trillions of dollars will be squandered and our economy destroyed.

The closing paragraphs from this article put all modelers, especially climate modelers, and their work in perspective:

“Li has been notably absent from the current debate over the causes of the crash. In fact, he is no longer even in the US. Last year, he moved to Beijing to head up the risk-management department of China International Capital Corporation. In a recent conversation, he seemed reluctant to discuss his paper and said he couldn’t talk without permission from the PR department. In response to a subsequent request, CICC’s press office sent an email saying that Li was no longer doing the kind of work he did in his previous job and, therefore, would not be speaking to the media.”

“In the world of finance, too many quants see only the numbers before them and forget about the concrete reality the figures are supposed to represent. They think they can model just a few years’ worth of data and come up with probabilities for things that may happen only once every 10,000 years. Then people invest on the basis of those probabilities, without stopping to wonder whether the numbers make any sense at all.”

However, while Li’s formula may be a small part of the current problems, I think an even bigger contribution has been the Black Scholes option pricing formula. This really did win a Nobel Prize, but for Myron Scholes and Robert Merton only, since Fischer Black had died prematurely before the prize was awarded.

While the formula is undoubtedly correct given its assumption that stocks are governed by Gaussian Brownian motions, but problem is that people have bought into the idea that because the solution was so elegant, the assumptions must be correct. The whole concept of a “hedge fund” that somehow makes clever trades that elminate risk is based on the Black/Scholes concept of a “hedge ratio.” It is no accident that Myron Scholes and Robert Merton went on to found the notorious Long Term Capital Management hedge fund.

However, Benoit Mandelbrot has long insisted that the “Paretian” stable distributions are better able to model the fat tails that are observed in practice for stock price movements etc. The Generalized Central Limit Theorem states that if the sum of iid contributions has a limiting distribution, the limit must be a member of the stable class. The Gaussian distribution is only one member of this class, the one with the shortest tails, and the only one with a finite variance.

A continuous time process with stable increments is full of discontinuities, unlike a Gaussian diffusion process, which is a continuous function of time. Most of these discontinuities are quite small, and just look like a diffusion. But occasionally a big one occurs. These are the events Taleb characterizes as “Black Swans”, but contra Taleb, they are mathematically quantifiable. See my 1978 J. Business paper.

I’ve done a lot of work with using stable distributions to model financial uncertainty, but there has essentially zero interest on Wall St. in this approach. See the recent papers on my webpage, and the references to earlier papers there. I’ll add some PDFs of these papers when I get a chance.

See especially my “Financial Applications of Stable Distributions”, Handbook of Statistics Vol 14, which develops an option pricing model for log-stable distributions, despite the misgivings of Samuelson and Merton on the feasibility of this. Also, my 1985 J Banking and Finance paper, which applies this model to the problem of evaluating deposit insurance for banks and thrifts. The same approach could be applied to counterparty risk on credit swaps, etc.

Speaking of his Gaussian copula function, Li himself said of his own model: “The most dangerous part is when people believe everything coming out of it.”

Recipe for Disaster: The Formula That Killed Wall Street

Nassim Taleb is quoted towards the end of this article. It is a very interesting read. You could almost substitute the words climate model for financial model in a few parts.

here is the reference 4 ya, its the last para.

http://www.edge.org/q2008/q08_17.html#taleb

havin read the book (unlike most of these commenters), i would suggest that Taleb is mainly attacking the statistical methods used by economists and social scientists…

Its a great read, altho i got bogged down a few times, and apparently it was the best selling non-fiction book on amazon for 2007.

i guess he has probly sold a few this year too!

For your info, this is his homepage…

http://www.fooledbyrandomness.com/

and the wiki with some good links

http://en.wikipedia.org/wiki/The_Black_Swan_(book)

“for socio-economic and other nonlinear, complicated variables, we are riding in a bus driven a blindfolded driver, but we refuse to acknowledge it in spite of the evidence, which to me is a pathological problem with academia”

(http://rs.resalliance.org/2008/09/17/financial-resilience-taleb-and-mandelbrot-reflect-on-crisis/)

I don’t know how well informed he is on climate change, but based on what I know this comment supports my extremely skeptical position.

So nice to see no reference for your quote!

In any event the quote makes no sense to me. What is “the most ecologically conservative stance”? What level of resources would one allocate to acheive that end. Moreover, if the black swan is unpredictable in both its nature and the time of occurance, how do we know if it is more or less likely to occur based on the action we take. Any action! It may only be the fact that we took action to acheive “the most ecologically conservative stance” that caused the black swan to occur.

On the other hand, sounds like a good idea.

“Correspondents keep asking me if it the climate worriers are basing their claims on shoddy science, and whether, owing to nonlinearities, their forecasts are marred with such a possible error that we should ignore them. Now, even if I agreed that it were shoddy science; even if I agreed with the statement that the climate folks were most probably wrong, I would still opt for the most ecologically conservative stance — leave planet earth the way we found it. Consider the consequences of the very remote possibility that they may be right, or, worse, the even more remote possibility that they may be extremely right.”

Nice to see 32 comments passed before someone stopped chin-stroking and actually found out what the man thinks!