On a hectic day on Wall Street, the

New York Stock Exchange's

storied trading floor can still make for great theater.

A televised shot of young traders muscling each other for position, frantically waving their arms and screaming at the top of their lungs remains the quintessential image of American capitalism at work.

It's also the NYSE's most honest public relations ploy, despite former Chairman Richard Grasso's attempt to turn the daily bell ringing at the start of the session into an over-the-top media event. For that reason alone, it's hard to imagine the Big Board ever completely ditching its 211-year-old tradition of being a face-to-face marketplace for buying and selling stocks.

(To see how close Grasso came to making that tradition permanent,

click here.)

But the NYSE, which is under pressure from institutional investors and securities regulators to rethink the way it does business, could take a lesson from the London Stock Exchange, another well-known stock market that found there is life beyond the trading floor, if there's a will to change.

Nearly two decades ago, the London, which is nearly as old as the NYSE, ditched its trading floor in a controversial move that's known in the European financial world as the "Big Bang." Trading was moved from brokers and specialized traders called "jobbers" on the trading floor to computers located in the offices of London brokerages.

In effect, the London evolved from a floor-based system to one that more closely resembled the

Nasdaq Stock Market

, which relies on dozens of trading firms, or market makers, to electronically execute buy and sell orders.

The evolution didn't stop there. In 1997, the London took another bold leap forward by ditching the middleman altogether and converting itself into a low-cost electronic trading network. Trading firms and market makers were replaced with a sophisticated computer system known as SETS that automatically matches buyers with sellers.

In effect, the London transformed itself into a giant electronic communications network, or ECN, that has helped reduce trading costs for investors. In fact, according to Elkins/McSherry, a securities industry consulting firm, the average cost of completing a trade on the London is now cheaper than on the NYSE or the Nasdaq.

Three years ago, the London also did something the NYSE is once again considering: It sold shares to the public. The move forced the exchange to clean up its act and adopt more open disclosure rules and reform its corporate governance practices.

To some degree, it's unfair to compare the London to the NYSE.

First, the European exchange is much smaller than its U.S. counterpart. On any given day, the London's computerized system processes 2.35 million trades a month, compared to 55 million on the NYSE. (The figure denotes transactions, not share volume.)

Second, the changes at the London came as the exchange was losing market share to other European exchanges. The NYSE, by contrast, is thriving despite its tarnished image in the aftermath of the Grasso pay debacle. The NYSE handles roughly 80% of the daily trading activity in Big Board stocks, a far better percentage than the Nasdaq, which has lost nearly half its market share to electronic rivals

Instinet

(INET)

and

Archipelago Exchange

.

"The London Stock Exchange had a system that was broken and wasn't working," said Maureen O'Hara, a professor at Cornell University's Johnson Graduate School of Management.

Securities experts also say a higher percentage of trades go unfilled in the London market than on the NYSE, especially in smaller, illiquid stocks. NYSE supporters note its specialists -- trading firms such as

LaBranche

(LAB)

,

Van der Moolen

(VDM)

and

Goldman Sachs'

(GS) - Get Report

Spear Leeds -- provide a buyer of last resort for a stock, something the London has eliminated with an all-electronic market.

"ECNs are great for matching up buyers and sellers when they are there, but when they aren't, sometimes all you can do is wait," said James Angel, a professor at Georgetown University School of Business. "That allegedly ancient, outmoded trading floor still does a better job than lots of other markets."

But London's transformation demonstrates that specialists, which currently control the trading running through the market, need not have their hands in every single transaction in order to have a cost-efficient and orderly market. Critics contend that the NYSE specialist system needlessly slows trading, especially when computers easily pair buyers and sellers with similar orders.

Specialist firms also face an ingrained temptation to abuse their exclusive franchise in the 2,800 listed stocks. They play a big role in setting prices for stocks, and because all buy and sell orders executed on the NYSE pass through them, they make most of their profit from trading stocks for their own benefit.

Specialists are not supposed to take advantage of their customers when they make proprietary trades. But critics have contended they have a built-in advantage since they know how everyone else trades in a given stock. Securities regulators are now looking into some of those allegations.

Many think there's no need for the NYSE to burn down the house and start from scratch like the London did. The Big Board could reinvent itself by building a model that combines the best of the specialist system with the speed of an electronic trading system. Just this week, a group of state treasurers and pension fund managers urged the NYSE to "incorporate successful models from other exchanges" as it tries to create a fairer market for all investors.

Indeed, the seeds of that transformation already may exist at the NYSE in its SuperDot computer system, which electronically routes roughly 75% of the buy and sell orders to the terminals of one of the Big Board's seven main specialist firms.

Under the current system, the specialist signs off on all trades on SuperDot, collecting a small fee in the process. But critics contend it wouldn't be difficult for the NYSE to transform SuperDot into a giant ECN, in the same way the SETS works on the London, and completely cut the specialist out of the process.

In one scenario, specialists might focus on harder-to-complete trades, ones involving either big blocks of shares or trades in small and illiquid issues. The role of the floor brokers, another intermediary, also could be reduced with an ECN handling most of the trading in Big Board stocks.

"They have the ability to create an electronic matching system," said Robert Gasser, CEO for

Nyfix

(NYFX)

, a provider of electronic trading technology. "They have the brand. They have the liquidity. They have the ability to say we are an ECN for all intents and purposes, and they could get away with it."

To do that, however, the leaders of the NYSE would have to stand up to the parochial interests of its well-entrenched members. Such a transformation would offend the NYSE's floor brokers, specialists and brokerage firms, all of which know how to use the system to their advantage.

But the danger of doing nothing could be far greater.