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.
So what is a copula? It’s a statistical model for determining correlation between different random distributions. Correlation is at the heart of the business of financial engineering — if you’re going to construct a CDO out of mortgage obligations, you’d better know the probability that all of them will default at once. Pricing risky assets — the problem the market got horribly wrong — rests on computing the correlation between rare events. Li’s formula had a deadly simplicity. Correlation was reduced to one parameter — it didn’t take into account the relationships between various loans that make up a pool. The correlation between two stocks may not be constant over time, but the copula formula treated it as if it were.
So is financial math evil? I’m inclined to think we need more of it, not less. A simple model was applied too enthusiastically by bankers who didn’t understand the quants — maybe we’d have been spared the current credit crisis if asset managers had more mathematical sophistication.
But read Salmon’s whole article; it’s very smart and very accessible.