Stocks rose on Monday as sentiment swung in favor of hope that European officials would find a way to cut Greece's debt and shore up European banks.

Shares rallied to session highs in the afternoon after a report said a plan to leverage money from the European Financial Stability Facility was in the works.

Based on the latest available data, the Dow Jones industrial average <.DJI> ended up 272.46 points, or 2.53 percent, at 11,043.94. The Standard & Poor's 500 Index <.SPX> was up 26.50 points, or 2.33 percent, at 1,162.93. The Nasdaq Composite Index <.IXIC> was up 33.46 points, or 1.35 percent, at 2,516.69.

(Reporting by Caroline Valetkevitch; Editing by Kenneth Barry)