The future for the S&P 500 gained 1.2% and that for the Dow Jones Industrial Average also was up 1.2%.
The price of bitcoin jumped 7.3% to $75,120.00.
Bond yields also surged, with the yield on the 10-year Treasury climbing to 4.46% from 4.28% on Tuesday.
In Asian share trading, Japan's Nikkei 225 index gained 2.3% to 39,341.44 while the Kospi in Seoul edged 0.2% lower to 2,570.94.
Australia's S&P/ASX 200 rose 0.9% to 8,207.50.
Hong Kong’s Hang Seng index fell 2.7% to 20,439.58, ending a three-day rally, as investors sought safe-haven assets amid the uncertainties surrounding the U.S. election. The Hang Seng Tech Index slipped 3.3%, while the Shanghai Composite index edged 0.1% higher, to 3,388.70.
“Positive outcomes for Harris are expected to boost Asian assets, while Trump gains may exert downward pressure,” Anderson Alves of ActivTrades said in a commentary.
Chinese markets have been among the most active in the region this week as leaders hold a meeting of the Standing Committee of the National People's Congress, the country's legislature.
The gathering is expected to deliver more moves to help spur faster economic growth and resolve mounting levels of local government debt. On Tuesday, upbeat comments by Premier Li Qiang about the potential for both fiscal and monetary policies helped lift share benchmarks in Hong Kong and Shanghai by more than 2%. Li also expressed confidence that China will attain its growth target of about 5% this year.
On Tuesday, U.S. stocks advanced as voters headed to the polls and fresh data showed the economy remains healthy.
The S&P 500 rose 1.2% to 5,782.76 and the Dow industrials climbed 1% to 42,221.88. The Nasdaq composite gained 1.4% to 18,439.17.
Markets worldwide are fixated on what the election will mean for U.S. economic, monetary and trade policy, as well as geopolitics. A split in Congress between political parties would complicate policymaking, and a change to a White House headed by former President Donald Trump could bring major changes to trade and other policies.
The S&P 500 has risen nearly 70% since the 2020 president election brought President Joe Biden into office. It rallied to records as the U.S. economy bounced back from the COVID-19 pandemic and managed to avoid a recession despite a jump in inflation.
Later this week, the Federal Reserve is due to make a decision on interest rates. The widespread expectation is for the U.S. central bank to cut its main interest rate for a second straight meeting.
In other dealings early Wednesday, U.S. benchmark crude oil lost 65 cents to $71.34 per barrel. Brent crude, the international standard, gave up 71 cents to $74.82 per barrel.
The U.S. dollar surged to 154.25 Japanese yen from 151.62 yen late Tuesday.
The euro slipped to $1.0733 from $1.0931.
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