Hong Kong was among the top regional performers, closing up 2.0 percent on hopes for interest rate cuts both in the United States and locally.
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European share prices were also up in opening trade.
"Asian shares are following Wall Street and recovered due to renewed sense that the Fed will solve this crisis," said Toshihiro Matsuno, equities research head at SMBC Friend Securities in Tokyo.
"Volatility remains but I think the volatility will start calming down. It will move in waves, with periods of volatility followed by relative calm," he said.
The Federal Reserve pumped more money into the market and Bernanke told a senator the central bank was "prepared to act as needed," raising hopes that the Fed will cut its key rate when it meets next month.
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