Bank One Corp. chief executive John B. McCoy, who built the Chicago-based bank into the fourth-largest bank holding company, unexpectedly quit yesterday after months of mounting problems at the bank's credit-card unit.

McCoy, 56, came under sharp criticism from Wall Street after problems at the card unit, First USA, forced Bank One to twice lower its earnings expectations, first in August and then again in November.

Wall Street cheered the move, sending Bank One shares up $3.37 1/2 to close at $33.37 1/2 on the New York Stock Exchange. Shares had been selling as high as $60.87 1/2 in July and had reached a 52-week low of $29.75 on Monday.

Financial analysts and industry experts said McCoy's resignation was an indication that Bank One's board was eager to resolve the bank's problems. "McCoy is a third generation of McCoys to manage Bank One, so the board must have been extremely disappointed with the performance of the company," said Rob Sharps, manager of T. Rowe Price's financial services fund.

Sharps predicted that the board will try "fix the company first" before it considers selling part or all of it to another financial institution.

With McCoy's departure, however, some analysts predicted that a merger or sale--both rumored since Bank One first warned of lower earning estimates--may be more likely.

"McCoy had backed the company against a wall, saying he would never consider a sale," said Anthony Polini, an analyst with Advest Inc. "Now that he's no longer at the company, it can think rationally and consider all alternatives."

Polini predicted a merger with another major financial institution, a sale or spinoff of First USA, or a sale of the entire company to another bank.

Bank One spokesman Thomas Kelly said the company's policy remains the same: "We intend to control our own destiny."

Bank One has promised to meet with financial analysts next month to lay out its strategy. Such a meeting had been scheduled for November, but Bank One abruptly canceled it after it issued its second warning of lower-than-expected earnings. Kelly said no date had been set for next month's meeting.

"The market is clearly voting that it is for this" management departure, said Diane Glossman, bank analyst for Lehman Brothers.

"The McCoy family was one of the greatest families in banking," Polini said. "Bank One was at its best buying college-town banks and transforming them into high-performance banks overnight."

But the company's current woes began with more aggressive acquisitions--its $7 billion purchase of First USA, the nation's second-largest credit-card issuer, in 1997 and its $19 billion buyout of First Chicago NBD Corp. a year later.

Bank One blamed lower earnings on problems at First USA, which accounts for one-third of the company's business. First USA was hit by increased competition and a series of aggressive pricing initiatives that drove customers away.

"Credit-card customers are increasingly fickle, and First USA alienated customers by jacking up fees and eliminating the one-day grace period for late payments," said David Robertson, president of the Nilson Report, which tracks the credit-card industry.

While Bank One searches for a new permanent chairman and executive, it tapped Verne G. Istock, 59, president of Bank One, as acting chief executive and John R. Hall, 67, a Bank One director and former chairman and chief executive of Ashland Inc., as nonexecutive chairman.

CAPTION: John B. McCoy came under sharp criticism from Wall Street.