By Cal Mankowski

NEW YORK (Reuters) - U.S. stocks rallied on Monday as JPMorgan Chase & Co (JPM.N: Quote, Profile, Research) increased its offer to buy Bear Stearns Cos BSC.N five-fold and data showed signs of a possible bottoming in the troubled housing sector.

The Nasdaq was up 3 percent, while the Dow and S&P 500 each climbed almost 2 percent.

Investors warmed to the higher offer for Bear Stearns, to about $10 (5 pounds) a share, as it may avert a long shareholder battle and let JPMorgan close the deal sooner.

Sentiment also was sweetened by a report from the National Association of Realtors, which said the pace of existing home sales in the United States in February showed a surprising rise. The Dow Jones home builder index shot up 9.2 percent.

The Standard & Poor's index of financial shares climbed 2.5 percent. Shares of JPMorgan rose 3 percent to $47.36, while Bear's shares more than doubled to a session high at $13.80 -- well above the new offer price.

"It seems like we're building a base and starting a rally," said Peter Jankovskis, director of research at OakBrook Investments LLC in Lisle, Illinois. "Maybe the market has bottomed here."

The revised terms of the Bear Stearns deal showed there was "more life to Bear than the people expected last week," he said.

Following strong gains last week, the Dow Jones industrial average .DJI rose 234.70 points, or 1.90 percent, to 12,596.02. The Standard & Poor's 500 Index .SPX gained 26.49 points, or 1.99 percent, to 1,356.00 and the Nasdaq Composite Index .IXIC rose 70.83 points, or 3.13 percent to 2,328.94.