Stocks rebounded sharply Tuesday as a drop in Spain's borrowing costs and unexpectedly strong economic data from Germany eased euro zone debt worries.

Short-term financing costs for struggling Spain more than halved as banks lapped up debt at an auction, apparently coming via cut-rate loans from the European Central Bank.

The successful auction helped alleviate investor worry about Europe's debt crisis and fueled the broad rally in equities, with each of the 10 major S&P indexes up more than 1 percent.

It's not just a question of just a bounce back off of what happened yesterday, which is part of it, but you are also seeing to a large degree some fear alleviated particularly because of the appetite for Spanish debt that was showcased in the overnight, said Peter Kenny, managing director at Knight Capital in Jersey City, New Jersey.

The U.S. is the relative darling for world markets and we get an inordinate amount of attention on the upside, when things in Europe stabilize, even if it's only momentarily.

Headlines and fluctuating European bond prices continued to spark high volatility. Stocks will be prone to large swings this week on expected low volume due to the upcoming Christmas holiday.

The Dow Jones industrial average <.DJI> surged 257.10 points, or 2.19 percent, at 12,023.36. The Standard & Poor's 500 Index <.SPX> was up 28.98 points, or 2.40 percent, at 1,234.33. The Nasdaq Composite Index <.IXIC> jumped 64.03 points, or 2.54 percent, at 2,587.17.

The S&P fell more than 1 percent on Monday, coming close to a key technical support level.

Networking stocks rose after AT&T Inc dropped its controversial bid for T-Mobile USA, the Deutsche Telekom unit as investors anticipate spending on wireless equipment would accelerate.

U.S.-listed shares of Alcatel-Lucent surged 10.8 percent to $1.54 and Juniper Networks Inc climbed nearly 10 percent to $19.86. The NYSEArca Networking index <.NWX> jumped 5.4 percent. AT&T shares edged up nearly 1 percent to $28.99.

On the economic front, U.S. housing starts and permits for future construction surged to a 1-1/2 year high in November as demand for rental apartments rose.

The Munich-based Ifo think-tank said German business sentiment rose sharply in December, defying expectations it would decline and underscoring the resilience of Europe's biggest economy.

The first-ever offer of three-year loans to banks from the European Central Bank on Wednesday is expected to be a strong indicator of whether debt-loaded countries get some relief or endure more pain.

(Reporting By Chuck Mikolajczak; editing by Jeffrey Benkoe)