The shares rose as high as $31.14, or 55.7 per cent above the IPO price, in early trading on the Nasdaq, at one point pushing the market value of the company to $19.9bn, before seeing the price ease later to $28.32.
As of early afternoon, Groupon had the second-highest trading volume on the Nasdaq, more than 39m shares.
But the price rise was in part due to the scarcity of its shares, as Groupon listed only about five per cent of its total share capital, or 35m shares, at $20 per share.
The $700 million raised was on the larger side for a US IPO, but the five per cent represented the second-smallest share float in the United States in the past decade, according to capital markets data provider Ipreo.
Groupon sells internet vouchers for everything from meals out to nose jobs, and is one of this year's biggest and most closely watched IPOs. A strong first few trading days could help other private internet companies - such as Angie's List, Zynga and even Facebook - to pursue their own IPOs.
There is a huge backlog of companies that filed to go public earlier this year. Most put their plans on hold when the stock market slumped in August. Groupon is the first major IPO since then.
Chief Executive Andrew Mason and Chairman Eric Lefkofsky hugged in Times Square after ringing the opening bell on the Nasdaq. Employees at company headquarters in Chicago donned lime green T-shirts emblazoned with the company's ticker symbol "GRPN" printed in old, ticker-tape-style lettering.
Some analysts and investors warn that Groupon's early surge could be a short-term phenomenon and its shares could reverse course and trade down like those of Internet radio station Pandora Media Inc.
There are still lingering questions about Groupon's business model and about competition from better-funded rivals such as Amazon.com Inc and Google Inc.
Groupon has lost two chief operating officers in the past year and had to adjust its accounting twice under regulatory pressure.
"They wanted to have a decent pop on the stock so they didn't take that much public," said David Berman, a consumer technology and retail specialist at hedge fund firm Durban Capital. "They created demand by limiting supply, and they got the pop."