Stocks surged more than 2 percent across the board Wednesday, with the Dow and S&P 500 logging their best one-day gains in 2012, amid growing hopes that central banks around the world will implement further measures to support the global economy.

Stocks saw an extra boost in the final minutes of trading after San Francisco Fed President John Williams said the central bank must stand ready to take even more policy action to boost the ailing job market.

The Dow Jones Industrial Average surged 286.84 points, or 2.37 percent, to close at 12,414.79, led by BofA , logging its first two-day win streak since late April.

The S&P 500 jumped 29.63 points, or 2.30 percent, to end at 1,315.13. The Nasdaq spiked 66.61 points, or 2.40 percent, to finish at 2,844.72. Both indexes are now out of correction territory. The CBOE Volatility Index, widely considered the best gauge of fear in the market, plunged almost 10 percent to end near 22.

All 10 S&P sectors closed firmly in positive territory, led by financials and energy.

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