Optimism has not been an emotion experienced by too many Europeans of late. Yet that positive feeling is creeping into the markets. The big stock exchanges in Europe are all off to strong starts this year: The Dax index of German stocks is up 16 percent. Even the Athens stock exchange is up 21 percent. The bond markets, meanwhile, are easing borrowing costs for Spain and Italy, with yields below 6 percent on 10-year bonds. An impressive performance, considering the euro crisis is far from over and a risk still exists that Greece won't have the money to pay bondholders come March 20.

So why the sunnier feelings? Investors have a lot of reasons, some of them contradictory. They all show how far Europe's markets have come since the onset of the crisis in late 2009. There are five in particular:

• The European Central Bank's newfound willingness to lend banks as much money as they want for three years is proving very effective in supplying Europe's financial system with extra liquidity. The longer-term refinancing operations (LTROs) allow Europe's banks to post iffy collateral-like the banks' holdings of Greek sovereign debt-with the ECB, which provides cheap loans in return. The three years are long enough to bridge the crisis, and the money gives the banks time to improve their balance sheets and boost their own lending, the ECB hopes.

David Fuller's view Obviously Europe's problems have not been resolved but they have been contained in ways that few people dared hope in 4Q 2011. That is a form of progress and it has been reflected by stock market performance.