SAN JOSE, Calif. — Square's stock rocketed above its initial public offering price by 45 percent on Thursday, capping one of the most closely watched debuts of a tech stock this year.

San Francisco-based Square jumped 45.2 percent higher on Thursday, or $4.07, and closed at $13.07.

The high-profile Silicon Valley start-up has endured a bumpy ride, starting with an IPO price of $9.

That IPO pricing was 22 percent below the estimated private valuation levels of around $15.46 at which Square had been selling its stock from 2014 onward.

San Francisco-based Square opened trading on Thursday at $11.20 a share, using ticker symbol "SQ" on the New York Stock Exchange. At one point, Square reached a high for the day of $14.78 but retreated from that peak level.

Some analysts questioned the timing of the IPO, but Square obviously disagreed.

"Now is the time, because you have a big platform shift in payments happening in the United States and we wanted to get that message out," Square Chief Financial Officer Sarah Friar said. "The time felt right, the momentum felt right."

Private investors were expected to closely scrutinize Square's first day of trading because they may be seeking signals about the viability of financing tech start-ups.

"Somebody has to invest and that venture fund is going to be much less likely to invest at these high valuations if they realize that investment might end up losing money," said Gil Luria, an analyst at Wedbush Securities.

But Square also faces tough questions from investors about how it will make a profit, expand its business beyond payments and Chief Executive Jack Dorsey's second job leading struggling social media company Twitter, pressure that only heats up after a company goes public.

On Wednesday, the company priced its IPO below its expected range of $11 to $13.

At its opening price Thursday, the company was valued at $3.9 billion including options. That's lower than the $6 billion valuation it received from its last private financing round.

The Square IPO was launched during a frosty atmosphere for initial public offerings in general, and an even more icy reception for IPOs launched by technology or Internet companies.