Bruised and battered by euro zone debt problems, the bloc's banks have come off the ropes and could double the 20 percent gains they have made in recent days if European leaders act decisively to end the crisis.

Euro zone banks are up nearly a quarter since late November on central bank moves to boost liquidity and free up funding markets as well as hopes for bold steps to stem the region's debt crisis that has been haunting investors for two years.

The STOXX Europe 600 Euro Zone Banking Index <.SX7E> hit a one-month high on Monday. It gave up some gains on Tuesday after Standard & Poor's threatened to downgrade 15 euro zone countries, but the index remained about 24 percent above a near three-year low hit late last month.

Although a possible downgrade by S&P in the event of a failure of EU leaders to reach a solid agreement to solve the crisis might pressure bond yields and bite into the value of banks with massive exposure to the region's debt, some investors have taken a positive bet on financials.

The index soared more than 15 percent last week and analysts see further gains if European leaders turn hopes into action.

Exposure to peripheral euro zone sovereign debt and fear of default or bankruptcy had combined with regulatory demands for extra capital buffers to push bank stocks sharply lower until last week's surge -- the biggest weekly gain since early 2009.

It's hope that Germany and other European countries will agree on some form of fiscal union, and the quid pro quo for that will be the European Central Bank stepping up more liquidity measures, Andrew Lim, banking analyst at Espirito Santo, said.

French President Nicolas Sarkozy and German Chancellor Angela Merkel agreed on Monday to push for closer union, ahead of a summit of European leaders on Friday.

The broader STOXX Europe 600 Banks Index <.SX7P>, which includes UK, Swiss and Nordic lenders, also jumped last week, by 13.8 percent, but is still down about 30 percent this year -- the worst-hit STOXX sector.

Banks reflect investor sentiment better than any other sector, Howard Wheeldon, senior strategist at BGC Partners, said. If the markets continue to lead, the banks may soon be back where they have been.

For Koen De Leus, strategist at KBC Securities in Brussels, however, betting on banks remained a binary risk, with the potential for a 20 percent gain or fall, depending on how this week develops.

The outlook for the region remained uncertain, he said, as recession fears mount and the hunt for additional capital intensifies. So after a rise of 20 percent I would get out since the coming recession in Europe will not make it easy to find additional capital.

Banks are a long term 'underweight' for me because they will be under fire from politics for the next five to 10 years.

Highlighting the depths of the sector weakness, the STOXX Europe 600 Euro Zone Banks Index has a price-to-book ratio of just 0.45 and 12-month forward price-earnings ratio of 6.25.

The P/B ratio divides a share price by the value of assets on a bank's books and, along with the price/earnings ratio, is a frequently used valuation measure for banks.

The wider STOXX Europe 600 <.STOXX> stocks index has a P/B of 1.4 and forward P/E of 10, Thomson Reuters data showed.

(Graphics by Scott Barber, additional reporting by Brian Gorman and Simon Jessop, editing by Nigel Stephenson)