European shares rose on Tuesday morning on optimism Greece was nearing a debt swap deal, while EU leaders agreed on a stricter budget discipline plan to prevent further debt build up in the region.

Earnings news was another boost for the market, with ARM Holdings (ARM.L) one of the top performers, rising 4.6 percent after fourth-quarter results beat forecasts.

The pan-European FTSEurofirst 300 .FTEU3 index of top shares was up 0.7 percent to 1,037.11 points at 0937 GMT, after ending at a two-week closing low on Monday. The index is up around 3.5 percent for January as a whole.

Banks, a focus in the euro zone debt crisis due to their exposure to euro zone peripheral debt, were among the best movers on the optimism over Greece, with the STOXX Europe 600 banks index .SX7P up 1 percent.

The banking index is up 9.9 percent so far this month and is on track to make its best monthly gain since July 2010, helped by the European Central Bank's decision to offer them cheap money.

Investor sentiment improved after Greek Prime Minister Lucas Papademos said debt swap talks had made significant progress. If a deal is not reached a messy default could occur which could send financial markets into turmoil.

Also helping the mood was an agreement on a fiscal pact by most European Union states which will impose quasi-automatic sanctions on countries that breach European Union budget deficit limits as well as a permanent rescue fund for the region.

They have made progress in Greece and the European leaders have endorsed the fiscal pact, said Mike Lenhoff, chief strategist at Brewin Dolphin Securities. There is optimism in the market.

It lowers the risk of instability to the financial system and company earnings. We are overweight defensive, but this is something that could make us change our portfolios as it diminishes the risk to the financial system.

British banks, however, were standout losers, with Lloyds Banking Group (LLOY.L), Royal Bank of Scotland (RBS.L) and Barclays (BARC.L) down between 1.3 to 2.4 percent, after Spain's Santander (SAN.MC) warned 2012 would be a tough year for UK banks and analysts cited ongoing political pressure in the UK.

The Euro STOXX 50 volatility index .V2TX, a key gauge of Europe's investor fear fell 4.6 percent as sentiment improved. The higher the volatility index, the lower investor appetite for risk.

It is down 20.1 percent so far this month, its biggest monthly decline since October 2011.

RANGE BOUND

Traders said that although investors were becoming more positive, the FTSEurofirst 300 index was stuck in a trading range between the 50 and 61.8 percent retracements of its sell off from February to September 2011 until there was a more certain outcome to the euro zone debt crisis.

The index, which pushed through the 50 percent Fibonacci retracement at 1,022.29 points in mid-January, was struggling to reach its next resistance level at the 61.8 percent retracement at 1,062.24.

There were concerns Portugal could be next in line to need a second bailout, with its 10-year bond yields surging to levels more than twice those considered unsustainable.

The next question on the horizon is Portugal, which seems likely to be the next potential hazard for the European Union, Rebecca O'Keeffe, head of investment at Interactive Investor, said.

The likelihood of default for Portuguese bonds is high; the credit swaps market is now pricing in a 72 percent chance of default for Portuguese bonds over the next 5 years.