SAN FRANCISCO » Square bounced back in its stock market debut today after the once-hot mobile payments service slashed the price of its initial public offering to get the deal done.

The 6-year-old company’s shares gained $4.07, or 45 percent, to close at $13.07. The surge helped ease the pain of a mortifying markdown in Square’s IPO price. The San Francisco company sold 25.7 million shares at $9 apiece after money managers leery of Square’s unprofitable history refused to pay $11 to $13.

The concession appeared to attract bargain hunters betting that Square is worth the price that its management team had been demanding in the IPO. Even with today’s rally, Square’s stock remains below the $15.46-per-share price that the company fetched a year ago when it raised $180 million as a privately held startup.

Most of the investors who participated in last year’s fundraising will be issued additional shares to compensate them for the reduced IPO price.

Another technology company, Match Group Inc., the owner of dating sites and apps Match.com, OkCupid and Tinder, gained 23 percent to close at $14.74 today. It had priced its IPO at the low end of its anticipated range

Investors’ skittishness toward Square, known for its debit and card readers that plug into mobile devices, reflects uncertainty about the direction of the global economy as the Federal Reserve Bank prepares to raise short-term interest rates for the first time in nearly a decade, said James Gellert, CEO of the research firm Rapid Ratings.

"Large, institutional investors taking a risk on technology want a discount now," Gellert said. "There is a lot of concern about more market volatility in the year ahead."

Square has been rapidly growing as millions of merchants have processed $32.4 billion in credit and debit cards through its readers and terminals during the year ending Sept. 30.

The company’s cut from the payment processing fees generated revenue of $893 million during the first nine months of this year, a 49 percent increase from the previous year. But Square has never turned a profit, accumulating losses totaling $527 million since its inception.

Some investors are also worried about the distractions and demands facing Square’s co-founder and CEO Jack Dorsey. Besides running Square, Dorsey is serving as CEO of Twitter at a time that the short messaging service is struggling to expand its audience and produce the first profit in its nine-year history.

Dorsey, who turned 39 today, has most of his wealth tied up in Square. His stake in Square is worth $930 million and his Twitter stake will be worth about $400 million after he turns over 6.8 million shares of his stock in that company to its employees.

The drop in Square’s market value over the last year could signal trouble ahead for other technology startups. With interest rates hovering near zero, venture capitalists and other investors have been pouring tens of billions of dollars into startups involved in transportation, data analysis, security, home rentals, finance and a wide assortment of other mostly mobile applications.

Dozens of these startups have been minted with market values of $1 billion or more in their fundraisings, a financial breed that has become known as "unicorns."

Many of them, though, are about to be exposed as "the donkeys that they really are," predicted Edison Investment Research analyst Richard Windsor. "In the long-term, a reset of valuations to realistic levels is a good idea but the journey to get there is always very painful."