NEW YORK, New York - U.S. stocks roared again on Tuesday with all the major indices notching up hefty gains.

"After falling more than 9% in September and extending its year-to-date decline to nearly 25% as of Friday's close, we think the S&P 500 was looking oversold," Mark Haefele, chief investment officer at UBS Global Wealth Management told CNBC Tuesday. "In addition, some of last week's selling pressure may have been driven by quarter-end rebalancing, which has now ended."

"With sentiment toward equities already very weak, periodic rebounds are to be expected," Haefelee added. "But markets are likely to stay volatile in the near term, driven primarily by expectations around inflation and policy rates."

The Nasdaq Composite led the way percentage-wise, surging 360.97 points or 3.34 percent to 11,176.41.

The Dow Jones industrials jumped 825.43 points or 2.80 percent to 30,316.32.

The Standard and Poor's 500 strengthened 112.51 points or 3.06 percent to 3,790.94.

On foreign exchange markets, the U.S. dollar was hammered. The British pound bounced to 1.1470 by the New York close Tuesday. The Japanese yen rose to 144.00. The Swiss franc was up sharply to 0.9794. The euro firmed to 0.9986.

The Canadian dollar rose to 1.3517. The Australian dollar edged up to 0.6500. The New Zealand dollar was stronger at 0.5730.

On overseas equity markets, the Paris-based CAC 40 soared 4.24 percent. The German Dax jumped 3.78 percent. In London, the FTSE 100 surged 2.57 percent.

On Asian markets, the Australian All Ordinaries was the star Tuesday, with the key index surging 248.90 points or 3.74 percent to 6,905.30. In New Zealand, the S&P/NZX 50 jumped 130.58 points or 1.19 percent to 11,090.03.

Japan's Nikkei 225 gained a hefty 773.43 points or 2.95 percent to 26,989.21.

In South Korea, the Kospi Composite added 54.55 points or 2.53 percent to 2,210.04.

Markets in mainland China and Hong Kong were closed for a public holiday.