A late frenzy on Wall Street led stocks to a sharp increase on Tuesday, even as fears over a major banking crisis in Europe mounted along with expectations that Greece could soon default on its debt.  The Standard & Poor’s 500-stock index spent most of the day in bear market territory, defined as a 20 percent drop from the recent peak. Less than an hour before the close, the index was down 1.9 percent. But in the final 49 minutes of trading it rose 4 percent after a report said European officials were discussing plans to recapitalize the Continent’s banks.  The Standard & Poor’s 500-stock index closed at 1,123.95, up 24.72 points, or 2.25 percent. The Dow Jones industrial average gained 153.41 points, or 1.44 percent, to 10,808.71, and the Nasdaq composite index rose 68.99 points, or 2.95 percent, to 2,404.82.  Analysts said that while the news from Europe might have been the immediate cause of the rally, the bigger story for the markets was their sustained volatility.  Investors remain jittery as they try to make sense of the debt crisis in Europe, an uncertain economic picture in the United States and a market that has fallen significantly, pushing stocks to levels that seem like bargain prices. In seven of the last 10 trading sessions, the Standard & Poor’s index has moved more than 2 percent.  “It’s almost a schizophrenic view from investors. Have we fallen off a cliff, or have we hit the bottom?” said Richard J. Peterson of Standard & Poor’s Capital IQ.  The rough ride will end only when some resolution is reached in Europe, Mr. Peterson said. But that day does not seem to be approaching very quickly. There are increasing signs that the economic situation in Europe is set to worsen.  The economy in the 17 countries that use the euro has already slowed to a standstill, and economists say they believe it could stay in a slump at least through the spring. There is widespread worry that austerity measures intended to reduce government debt will further choke Europe’s economies.  The price that European governments pay for credit-default swaps, which serve as insurance against default for their sovereign debt, rose sharply across Europe. After the markets closed in New York, Moody’s downgraded its outlook on Italian government bonds.  Interest rates rose slightly on Tuesday. The Treasury’s benchmark 10-year note fell 20/32, to 102 25/32, and the yield rose to 1.82 percent, from 1.75 percent late Monday.  Earlier in Europe, stocks declined sharply. In London, the FTSE 100 index fell 2.58 percent, the DAX in Frankfurt was 2.98 percent lower and the CAC 40 in Paris was down 2.61 percent.  Finance ministers from the 17 European Union nations that use the euro postponed moves to release the next installment of aid to Greece, which means that Greece will probably not receive the 8 billion euros ($10.6 billion) before November.  European banking shares fell sharply, led by Dexia, a financial concern based in Brussels whose value has plunged this week because of its exposure to Greek debt.  Traders pinned the late surge in United States stocks to a report on The Financial Times Web site that European Union finance ministers were looking at ways to reinforce the capital reserves of Europe’s banks as part of a broader move to contain the crisis.  Earlier, Ben S. Bernanke, the Federal Reserve chairman, voiced concern about the American economy when he addressed a Congressional committee. Mr. Bernanke called on Congress to take action on jobs, but also said that the Fed was prepared to make further moves to stimulate the economy. He said the turmoil in the markets was acting as a drag on the American economy.  Analysts noted the negative tone of his remarks.  “We’re no longer comparing it to what you would be expecting in a recovery — it’s that we’re not as bad as we were in 2008. He talks about the limits of what he can do,” said Eric Green, chief economist at TD Securities.  In economic data, new factory orders were down slightly in August, but not as bad as most analysts had predicted, according to figures from the Commerce Department.  Andrew Wilkinson, chief economic strategist for Miller Tabak & Company, said that the numbers were the latest in a series of economic indicators showing that the American economy was not slipping into recession. “It’s moving in the right direction, but it’s moving at a very slow pace,” he said.  Still, economists see the slowing economy in Europe as a troublesome sign for the United States. After the 2008 financial crisis, the American economy was fueled in part by exports. Interruptions in worldwide demand could cut off that road to recovery. A strengthening dollar could also be a concern, because it makes American exports more expensive.  The dollar rose to a fresh nine-month high against the euro, which fell as low as $1.3144, before recovering to $1.332.
A hopeful report on European banks prompted a late rally after the Standard & Poorâs 500-stock index officially traded in bear-market territory much of the day.