As the crisis has worsened over the last 18 months, pronouncements of plans to fix the euro zone debt problems have led to more than a half-dozen rallies that just as quickly withered as the proposals fell short of hopes.

Wednesday’s rally was among the biggest yet, with the three main indexes on Wall Street rising 4 percent or more, and the Dow Jones industrial average rising 490.05 points, its largest gain since March 23, 2009. Still, some analysts warned that the central banks’ action addressed only some symptoms of the euro financial crisis, so this rally, too, could evaporate.

“It helps to prop up the banks for a while which is going to buy time for Europe to fix the problem,” Burt White, the chief investment officer for LPL Financial, said. “This is basically a Band-Aid.”

Financial shares in particular were lifted by the news.

Bank of America shares, which on Tuesday fell more than 3 percent, to $5.07, their lowest closing level since March 2009, were up 7.3 percent, at $5.44, on Wednesday. JPMorgan rose more than 8 percent to $30.97. Morgan Stanley was up more than 11 percent at $14.79.

On Wednesday, the Federal Reserve, the Bank of England, the European Central Bank, the Bank of Japan, the Bank of Canada and the Swiss National Bank, trying to bolster financial markets as the euro zone debt crisis grinds on, announced that they would reduce by about half the cost of a program under which banks in foreign countries could borrow dollars from their own central banks, which in turn get those dollars from the Fed. The banks also said that loans would be available until February 2013, extending a previous deadline of August 2012.

The move is intended to free up liquidity and ensure that European banks have funds during the sovereign debt crisis. But some analysts saw it as a stop-gap measure to avoid a looming crisis that some compared to that set off by the collapse of Lehman Brothers in 2008.

“What it does do is take off some of the pressure from this boiling pot,” Mr. White said.

As the exuberance set in and funding pressures appeared to ease, bond prices fell, commodity prices rallied and financial shares soared as investors bought shares on the hope that the central banks had smoothed the way for Europe to take more forceful action in advance of a European summit meeting Dec. 9. The jump in stocks was also an extension of the turmoil and volatility that have characterized global markets for more than a year.

It was unclear even after Wednesday’s move whether banks would loosen up lending or whether the market enthusiasm would last.

Some noted sharp gains in equities in previous trading sessions have often failed to carry through, as European leaders had tried many times over the last two years to stave off a deterioration in the debt crisis. A recent attempt was on Oct. 27, when the broader market as measured by the Standard Poor’s 500-stock index rallied 4 percent on the hope that a new European plan could solve its problems. But it failed to sustain its gains.

That rally was one of eight times that the S. P. had spiked up at least 4 percent since the end of 2008, while in the same period it experienced 10 declines of that size.

In addition, a summit meeting in July caused a global stock rally that collapsed in the subsequent days, with the S. P. eventually sinking to its lowest level for the year.

Analysts were skeptical about whether Wednesday’s market enthusiasm would endure, and they also warned that the central banks’ move addressed only some symptoms of the euro zone financial crisis. Stanley A. Nabi, chief strategist for the Silvercrest Asset Management Group, said the coordinated action on Wednesday signaled that the problem had reached a crisis point, and that the central banks recognized there was a “lot of danger” in letting the current situation continue.

Steve Blitz, the senior economist for ITG Investment Research, said the central banks “are going to do what they can to ring-fence the European financials’ problems and keep them inside Europe.”

“They are trying to prevent them from seizing up global liquidity and capital flows and impacting banks and financial institutions throughout the world,” he said.

The S. P. 500-stock index closed up 51.77 points, or 4.33 percent, at 1,246.96. The Dow was up 4.24 percent, to 12,045.68, and pushed into positive territory for the year and for the month of November. The Nasdaq composite index rose 104.83 points, or 4.17 percent, to 2,620.34.

Interest rates were higher. The Treasury’s benchmark 10-year note fell 24/32, to 99 12/32, and the yield rose to 2.07 percent, from 1.99 percent late Tuesday.

Ralph A. Fogel, head of investment strategy for Fogel Neale Wealth Management, said rates would probably remain low.

As for equities after the central bank announcement, Mr. Fogel said “the fear is off that there is going to be any sort of tremendous move down like there was in 2008,” referring to the financial crisis.

Analysts said they believed the central banks’ action targeted one of the symptoms, rather than the root or cause, of the euro zone problems.

Energy, materials and industrial sectors all powered ahead by more than 5 percent.

The dollar fell against an index of major currencies. The euro rose to $1.3433 from $1.3328.

The Euro Stoxx 50 closed up at 4.3 percent, and the CAC 40 in Paris ended up 4.2 percent, while the DAX index in Germany was up almost 5 percent. The FTSE 100 in London rose 3.16 percent.

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