For hundreds of years, the way to solve problems in the financial market was clear: Get Wall Street’s titans in one place and knock heads. It took only 24 brokers gathered under a buttonwood tree to form what became the New York Stock Exchange.  J. Pierpont Morgan locked several dozen bankers inside his famous library on Madison Avenue to solve the panic of 1907. And in 1998, New York Fed president William McDonough convened representatives from the biggest Wall Street firms, 14 of which then bailed out Long-Term Capital Management.

Less than a decade later, financial markets have become vastly more complex. And they are no longer in the hands of a select few. Markets are tied together in ways that regulators and even Wall Street professionals struggle to comprehend. Bonds are bound to stocks, which are tied to currencies around the world.

The binding threads are derivatives, and the brightest minds on Wall Street worry about how they work—especially as stock markets around the world hit a bump. The term derivatives describes an array of financial contracts whose value is deter­mined by, or derived from, an underlying asset such as a stock or currency. The deriva­tives market, one of the fastest-growing areas of finance, is estimated at $300 trillion. A subset of that—credit default swaps, which are derivatives based on com­panies’ creditworthiness—last year reached $26 trillion, twice the size of the U.S. economy.

In their most benign form, derivatives are probably the greatest financial innovation of the past 25 years. They have helped smooth currency and interest-rate fluctuations by allowing investors to protect themselves. But when it comes to the really big stuff—such as global market collapses—derivatives could turn from vaccine to contagion. Investors use them as a form of insurance, which may give a false sense of security. “A financial crisis is likely to be a global event, not a local event, and derivatives will probably help make that happen,” says Joe Brandon, C.E.O. of General Re, a reinsurer owned by Berkshire Hathaway.

Brandon has grown intimately familiar with the perils of derivatives during a grand five-year experiment conducted on orders from his boss, Warren Buffett, to close Gen Re’s derivatives business.

Gen Re got into derivatives dealing in 1990 and became tied to global financial markets in ways it found difficult to predict. When Buffett bought the company in 1998, he quickly decided he wanted out. At Buffett’s behest, Brandon embarked on a task that lost Berkshire and Gen Re a cool $409 million before taxes. The experience led Buffett to write in his 2002 letter to Berkshire Hathaway shareholders what has become the most memorable line about the instruments: “Derivatives are financial weapons of mass destruction, carrying dangers that, while now latent, are potentially lethal.”

It may be one of the Oracle of Omaha’s pithiest pronouncements, but it’s also been one of the most ignored, as the derivatives markets have gone supernova. Even so, their vulnerability was reinforced this spring, when the market for mortgage securities, a type of derivative, seized up.

Yet investors remain oblivious at their peril. After all, two of the world’s smartest financial players, Buffett and Brandon, took lumps getting out of a modest derivatives business in some of the most placid waters financial markets have seen in years. Would J.P. Morgan Chase, Citigroup, or Goldman Sachs, all of which have vastly bigger derivatives businesses, have come out better?

Gen Re’s business was conservative. Yet it still lost money, with only a tiny percentage of trades piling up huge losses. Roughly 98 percent of its deals were fine. That suggests that when there are problems in a derivatives portfolio, they will be harder to discover, because of their rarity.

Much of Gen Re’s divestiture was conducted by Matt Nelson, a 42-year-old trader. He saw his role as a mix of chess grand master and private detective. He spent hours tracking down and persuading investors on the other side of the trades to work with him to get rid of the derivatives.

The General Re unit started out with more than 23,000 trades worth just under $1 trillion. The losses from excising those trades accounted for about half of Gen Re’s total loss. But even that overstates the story. In ditching the portfolio, Gen Re ended up making a modest amount on most contracts. It was a mere 500 trades that accounted for more than $200 million of the losses. The toxic 500 fell largely into one basket: complex foreign-exchange agreements. These were often contracts that spanned periods of 30 years or more and involved bets on both interest rates and multiple currencies. For example, Gen Re brought together Japanese retailers (who had become fed up with low returns in their local market) with all sorts of lending agencies, such as the World Bank. Gen Re hedged those trades with offsetting contracts pegged to moves in interest rates and currencies over several years. But because of what was essentially a math error, the hedges were inadequate.

Gen Re quickly learned that even without math mistakes, the squirrelly real world can throw off a sound financial model. In one set of trades, Gen Re figured it had found a bit of treasure. It entered into contracts involving the U.S. dollar, using what’s called a Bermudan swap option. These contracts were theoretically worth more than another common option because an investor could get out of them at multiple points in the future rather than at a single fixed date.

That’s the theory, anyway. When Gen Re went to unwind its trades, it couldn’t capture the extra value that its Bermudan swap options were supposed to have. “The models we used were simply models,” says Nelson. “They didn’t take into account real-life situations.”

The accounting for derivatives lends itself to bad numbers, even in the absence of malfeasance or sloppiness. At one point, Brandon reviewed the derivatives unit’s business over the past 10 years. During that period, it recorded about $1.2 billion in trading revenue and $505 million in operating income before taxes. It also set aside reserves in case things went badly. Gen Re’s auditors even wondered if the division was putting too much aside. But its reserves turned out to be insufficient. In Brandon’s analysis, the unit generated a third less income than had been anticipated. How did it go so wrong? Profit estimates for derivatives are susceptible to overstatement, in part because many of the contracts extend years into the future.

The irony (or perhaps hypocrisy) is that Buffett still uses derivatives. His famous declaration was “a lovely phrase, and it got him more ink than he could ever have hoped for or imagined,” says Jim Grant, who edits Grant’s Interest Rate Observer. “But to judge by his own investment record, he didn’t take himself literally. Nor should we take it literally. Credit default swaps and other derivatives are neither inherently good nor bad but desirable or undesirable at a price.”

Grant gets support for this theory from an authoritative source: Buffett himself. In a recent letter, released in early March, he wrote about the derivatives Berkshire Hathaway has entered into. “Why, you may wonder, are we fooling around with such potentially toxic material?” His answer: “Derivatives, just like stocks and bonds, are sometimes wildly mispriced.”

There you have it. There’s nothing intrinsically scary about derivatives, except when the bad 2 percent blow up. Derivatives are vulnerable to problems because the accounting is complex and they can add much more leverage to the system than investors realize. For derivatives to become dangerous, they need complacency.

That’s exactly what’s going on today. In February, a presidential panel led by Treasury Secretary Henry Paulson said hedge funds—among the heaviest users of derivatives—should remain lightly regulated. And the European Union’s chief market regulator similarly declared that no extra private equity regulations were needed. So, sure, derivatives aren’t inherently evil. But in the hands of overmatched regulators and blithe investors, they will be.