NEW YORK — John Phelan, who led the New York Stock Exchange into the modern era of competition and huge trading volumes and provided calm at the center of the storm when stock prices crashed in October 1987, has died. He was 81.

Mr. Phelan died on Saturday, according to a statement Sunday from Duncan Niederauer, chief executive officer of what is now NYSE Euronext.

‘‘John was an extremely generous and caring individual, and as chairman of the New York Stock Exchange and throughout his career John served our capital markets, investors, and all market participants with outstanding professionalism, commitment, and integrity,’’ Niederauer said.

From 1975 through 1990, as vice chairman, president, and then chairman, Mr. Phelan steered the stock exchange through a sometimes painful period of growth, modernization, and change.

Particularly affected were the specialists — brokers assigned to maintain fair and orderly markets by overseeing trading in specific stocks at posts on the exchange floor. As large securities firms carried out their own trades of large blocks of stocks, and electronic trading began matching buyers and sellers automatically, the specialist’s once-preeminent role was forever changed.

A onetime floor specialist himself, Mr. Phelan used his deep history and personal ties to nudge the exchange’s old guard to open up what had long been a close-knit club.

During his tenure, the exchange spent hundreds of millions of dollars on technology to make trading swifter and less prone to error. It joined the computerized Intermarket Trading System, which showed real-time bid and “ask’’ prices not just on the NYSE but also on regional US exchanges.

In 1986, Mr. Phelan began warning of a possible meltdown in stock prices. His concern was sparked by the growing popularity of both portfolio insurance — stock-index futures used to hedge positions — and trading by computer programs.

‘‘This whole business of portfolio insurance and program trading was adding a magnitude of leverage that hadn’t been seen in the modern marketplace,’’ he told Eric J. Weiner for ‘‘What Goes Up,’’ a 2005 book on Wall Street history.

The meltdown Mr. Phelan sensed coming arrived on what became known as Black Monday, Oct. 19, 1987, when the Dow Jones Industrial Average lost 508 points, or 22.6 percent. As equities plummeted, Mr. Phelan was among the public figures whose words and actions were closely watched by a worried investing public. ‘‘That was his shining hour,’’ Felix Rohatyn, managing director of Lazard Freres & Co., told The New York Times in 1990.

Even before trading opened that Monday morning, Mr. Phelan summoned the heads of major firms to his office. Based on the market’s weak performance the previous Thursday and Friday, and a flood of sell orders received over the weekend, he prepared for a difficult day.

‘‘I said we expected a weak market with high volume, and that we were opening all the systems early,’’ he recalled in a 2007 paper for a Black Monday symposium held by the Securities and Exchange Commission Historical Society. ‘‘I added, ‘No matter what happens, the exchange will stay open.’ We would shut down individual stocks if severe imbalances occurred in them. We would then indicate their new bid and offer prices and get them open again. But under no circumstances would we close the exchange.’’

Arthur Levitt, who was chairman of the American Stock Exchange at the time, said Mr. Phelan called him at one point that day to report the New York Stock Exchange was in fact about to halt trading. Mr. Phelan called back to say there would be no halt, Levitt said.

At 4:30 p.m. in New York, 30 minutes after trading ended for the day, Mr. Phelan held a press conference with other exchange officials. His choice of words and confident tone would draw widespread praise.

‘‘I don’t think the word ‘panic’ is correct,’’ he told one reporter. Asked his opinion on the cause of the selloff, he said ‘‘five years of a bull market without a correction,’’ plus higher interest rates and expectations of higher inflation, had ‘‘hit a very nervous market.’’

Tim Metz, in his 1988 book on the crash, “Black Monday,’’ wrote of the press conference: ‘‘This is a time for statesmanship, for class. And [Mr.] Phelan is at the top of his game.’’

‘‘His voice is steady, and his delivery clearer and less hurried than the New Yorkese he speaks offstage,’’ Metz wrote. ‘‘Far from seeming frightened or even nervous, he projects an offhandedness that no one would take for studied. The worst disaster in stock market history and [Mr.] Phelan is practically laconic about it. The image is perfect.’’

The next day, with losses continuing into late morning, Mr. Phelan walked to the trading floor and found ‘‘a stillness there,’’ he told Weiner. ‘‘It was almost as if everybody was in a daze.’’

He assembled his floor directors and reminded them of the need to keep the exchange open. ‘‘They were to continue to shut down stocks with imbalances, put up new bids and asks, and then reopen them,’’ he recalled in his SEC retrospective. ‘‘The future of the NYSE depended on their doing this.’’

The market turned around in the afternoon, helped by companies announcing stock-buyback initiatives, and the Dow ended the day up 102 points.

For much of the remainder of his tenure, Mr. Phelan was involved in reviews of Black Monday and the implementation of tools, such as so-called circuit breakers, to interrupt a crashing market. When a presidential commission headed by Nicholas Brady — soon to become Treasury secretary — criticized exchange specialists for not buying aggressively enough during the selling frenzy, Mr. Phelan came to their defense.

‘‘You don’t require a dealer to be a net purchaser,’’ he told The New York Times in 1988. ‘‘All we require is that they be in there, functioning.’’