Good theory. The glitch was discovered only after the fact: When a market is crashing and no one is willing to buy, it's impossible to sell short. If too many investors are trying to unload stocks as a market falls, they create the very disaster they are seeking to avoid. Their desire to sell drives the market lower, triggering an even greater desire to sell and, ultimately, sending the market into a bottomless free fall. That's what happened on October 19, 1987, when the sweet logic of Black-Scholes was shown to be irrelevant in the real world of crashes and panics. Even the biggest portfolio insurance firm, Leland O'Brien Rubinstein Associates (co-founded and run by the same finance professors who invented portfolio insurance), tried to sell as the market crashed and couldn't.

Oddly, this failure of financial theory didn't lead Wall Street to question Black-Scholes in general. "If you try to attack it," says one longtime trader of abstruse financial options, "you're making a case for your own unintelligence." The math was too advanced, the theorists too smart; the debate, for anyone without a degree in mathematics, was bound to end badly. But after the crash of 1987, individual traders at big Wall Street firms who sold financial-disaster insurance must have smelled a rat. Across markets—in stocks, currencies, and bonds—the price of insuring yourself against financial disaster rose. This rise in prices and the break with Black-Scholes reflected two new beliefs: one, that huge price jumps were more probable and likely to be more extreme than the Black-Scholes model assumed; and two, that you can't manufacture an option on the stock market by selling and buying the market itself, because that market will never allow it. When you most need to sell—or to buy—is exactly when everyone else is selling or buying, in effect canceling out any advantage you once might have had.

"No one believes the original assumptions anymore," says John Seo, who co-manages Fermat Capital, a $2 billion-plus hedge fund that invests in catastrophe bonds—essentially bonds with put options that are triggered by such natural catastrophes as hurricanes and earthquakes. "It's hard to believe that anyone—yes, including me—ever believed it. It's like trying to replicate a fire-insurance policy by dynamically increasing or decreasing your coverage as fire conditions wax and wane. One day, bam, your house is on fire, and you call for more coverage?"

THE PROBLEM

This is interesting: The very theory underlying all insurance against financial panic falls apart in the face of an actual panic. A few smart traders may have abandoned the theory, but the market itself hasn't; in fact, its influence has mushroomed in the most fantastic ways. At the end of 2006, according to the Bank for International Settlements, there were $415 trillion in derivatives—that is, $415 trillion in securities for which there is no completely satisfactory pricing model. Added to this are trillions more in exchange-traded options, employee stock options, mortgage bonds, and God knows what else—most of which, presumably, are still priced using some version of Black-Scholes. Investors need to believe that there's a rational price for what they buy, even if it requires a leap of faith. "The model created markets," Seo says. "Markets follow models. So these markets spring up, and the people in them figure out that, at least for some of it, Black-Scholes doesn't work. For certain kinds of risk—the risk of rare, extreme events—the model is not just wrong. It's very wrong. But the only reason these markets sprang up in the first place was the supposition that Black-Scholes could price these things fairly."