When things go seismic deep in the global economy, stock exchanges around the world react like so many volcanoes. From New York’s Wall Street to Tokyo’s Kabutocho district, their eruptions are the manifestations of trillion-dollar forces roiling under the surface, spouting volatility, and creating panic in a global market gone Vesuvius.

When things go seismic, watch out for the metaphor hose-down from economists, journalists, and shrieking CNBC V.J.’s trying to convey a picture bigger than what you can see by just riding the three-digit updrafts and free falls. In a delicate balance of dependence and autonomy, the exchanges of the world constitute tangible grounding mechanisms for spooked investors. They are rooms in which buyers and sellers trade by sets of rules that are, in the end, all that keep the global market from dissolving into chaos after each morning bell. The stability flows from how each market is simultaneously connected to the shifts of global capital yet also able to generate transactions on its own local terms.

An exchange must assure two things: that all serious buyers and sellers are represented and that the products of all sellers are deliverable and of some demonstrable quality. The same assurances are required whether cattle are changing hands in Argentina or shares of Sultan Center Food Products are being traded in Kuwait.

On a quiet, tree-lined street in Kathmandu—just up the road from the Freak Street market, fragrant with spices and diesel fumes and mountain-trekking hippies—sits the Nepal Stock Exchange. Beneath whirring fans, traders scrawl on whiteboards their “bids” and “asks,” worth about a million dollars a day, for such companies as Everest Bank and Butwal Power.

Meanwhile, the New York Stock Exchange, the biggest of them all, carefully maintains the elaborate illusion of a bustling trading floor, even though that space functions mostly as a TV studio and tourist attraction for visiting V.I.P.’s unaware of the vast computer networks that actually handle the transactions. An average of $100 billion worth of trades clears this legendary center of finance daily—only a quarter of the money that circulates through the world’s markets every 24 hours.

Electronic trading knows no geographic constraints, so nowadays stock exchanges can be found in places better known for thousand-year-old eggs than for nest eggs. The explosion of trading across the globe has created wealth in some of the most persistent pockets of poverty and produced waves of volatility, as when this year’s U.S.-subprime-mortgage tsunami hit beaches in South Korea, Australia, and Indonesia. In an era when billions zip from continent to continent in milliseconds, it is exhilarating to recall that modern capitalist economy is built on a mysterious faith that, in the public forum of the exchange, the other guy or gal is not going to screw you. An absence of trust has plagued one of the world’s smallest stock exchanges, in Douala, Cameroon. Haunted by the country’s enduring reputation for corruption, the Douala exchange has hosted trades in shares of only one company—a local bottled-water producer—since opening in April 2003. Meanwhile, the end of a corrupt dictatorship has produced a boom in Kenya. There are more ways than ever for U.S. investors to chase those returns: One can give cash directly to a non-U.S. broker or buy one of a dizzying array of securities, such as shares in specially structured mutual funds. The Federal Reserve estimates that U.S. investors hold more than $4 trillion worth of foreign equity, much of it in emerging markets in Asia and Latin America.

While most economists were caught off guard by this year’s trading volatility, the modern exchange is capable as never before of weathering sudden big moves. New regulations make it easier to figure out the real value of what’s being traded. This transparency is essential in an instantaneous-trading environment, where an Enron’s value can be carefully manufactured over a period of years and then vaporized in a single catastrophic week. The Sarbanes-Oxley Act, for example, was intended to reveal and manage risk. But such regulations, in turn, create opportunities for markets with fewer rules.

Witness the London Stock Exchange’s aggressive pursuit of initial public offerings from companies in Asia. Last year, London became the world leader in I.P.O.’s. And while global markets were rocked in the summer’s subprime hysteria, Shanghai barely registered a blip. China’s vast emerging economy was big enough to absorb the blows, suggesting that the game is changing big-time. The future will belong to the market that can set up the biggest tent for investors who want to manage and chase risk. Having purchased Archipelago Holdings and Euronext, the NYSE Group considered excising “NY” from its name to emphasize a more global coverage. Many economists think that would have been absurd. “There will always be value in having the best reputation for risk management,” says Ev Ehrlich, former Commerce Department undersecretary. “New York is a brand, and the volatility of emerging markets will only enhance that brand as traders get burned in an unregulated environment.”

Yet stepping outside traditional regulations is emblematic of our volatile age. New wealth, much of it in private equity, is following risk and opportunity faster than new exchanges can pop into being. At the same time, companies in emerging markets are scrambling to gain access to mainstream capital, which has accelerated the trend toward multiple listings of stocks on exchanges all over the world. “Technology makes it cheaper and easier to do,” Ehrlich says. We may soon have one global market in which all buyers and sellers gather to purchase virtually any stock or commodity. There will be no single picture of that market. Even from space, you can see only one side of the earth at a time. That’s probably just a silly detail, but it’s no metaphor. Yet while no camera will ever be able to see the whole world at once, savvy global traders have to. Between the first open in New Zealand and the last close on the U.S. West Coast are 19 time zones of financial daylight. That leaves just five hours for uneasy dreams about what will happen tomorrow. Until someone opens an exchange in Samoa.