Analysts are so bullish on facebooks mobile advertising prospects because

(Adds analysts’ comments, details on game announcement, background)

SAN FRANCISCO, July 30 (Reuters) - Facebook Inc’s stock on Tuesday came within a hair of reclaiming its $38 debut price for the first time since going public in 2012, a milestone in the social networking company’s effort to wipe away Wall Street’s skepticism of its business.

The stock has surged more than 40 percent in the past week after the company reported blowout quarterly results that showed Facebook’s progress building a mobile advertising business.

Shares of Facebook climbed as much as 7 percent to $37.96 in heavy trading on Tuesday, before settling back to finish the regular session at $37.63.

The social network, with 1.15 billion users, has never traded at or above $38 since its initial public offering in May 2012.

Facebook’s market value was cut in half in the months following the IPO as concerns about issues ranging from slowing revenue to massive insider selling made the Internet company’s stock a Wall Street punch line.

“Most companies of that size don’t re-accelerate their growth rate. Facebook’s been an exception,” said Aaron Kessler, an analyst with Raymond James.

“I would say they’re in better shape today than they were at the IPO price and the stock is still below that,” he said.

Facebook options volume was frenzied on Tuesday, as overall turnover was 3.8 times the recent daily average, according to options analytics firm Trade Alert. Traders on Tuesday exchanged 694,000 calls and 300,000 puts on Facebook.

The most popular options were the weekly $38 and $37 strike calls expiring this Friday as most traders expected gains in coming days.

One player liked the weekly $32.50 strike puts expiring on Aug. 9 which appeared to be bought 15,000 times for only a dime, said WhatsTrading.com options strategist Frederic Ruffy.

Facebook’s recent success building a mobile advertising business - an area where many of its rivals have struggled - and the online service’s expanding number of daily users have won back investors’ respect and confidence in its prospects. That has fueled a rebound in the shares, which are up more than 50 percent in July.

Facebook said last week its mobile advertising revenue grew 75 percent in a span of three months, trouncing analyst targets and delivering the company’s strongest revenue growth since the third quarter of 2011.

Many analysts raised their price targets above the $38 level following Facebook’s quarterly report last week.

The second quarter results “were really a game-changer in terms of how Facebook is perceived on the Street,” said Pacific Crest Securities analyst Evan Wilson. “It was pretty close to the perfect quarter.”

Facebook announced plans on Tuesday to help market and distribute mobile games on its social network in exchange for a cut of revenue that the games generate, raising hopes that the company could tap a new business.

And many investors expect Facebook to offer high-priced video ads in the coming months.

ERASING DOUBTS

Created in a Harvard dorm room by CEO Mark Zuckerberg in 2004, Facebook become the first American technology company to debut on Wall Street valued at more than $100 billion.

Facebook’s IPO was to have been the culmination of eight years of breakneck growth for a company that became a social and cultural phenomenon. Instead, it was marred by a series of trading glitches on its debut, and the company and its underwriters subsequently faced accusations of pumping up the price and inadequate disclosure.

Facebook shares opened 11 percent above the $38 offering price on May 18, 2012. But a series of problems that plagued the Nasdaq Stock Market where the shares debuted contributed to a sharp fall in the stock after it peaked that day at about $45. It closed at $38.23, and on the following Monday shares fell through the $38 price.

By early September, Facebook’s shares bottomed at $17.55.

The cool investor reception to Facebook and other consumer dotcom debutantes at the time, such as Groupon Inc to Zynga Inc, put a chill on the Silicon Valley IPO train.

“The question has never been do a lot of people go to Facebook. The question is how much revenue and profitability can Facebook derive from that activity,” said Pacific Crest’s Wilson.

“There have been many that have questioned whether or not Facebook would grow significantly, but Q2 kind of erased that doubt,” he said, referring to Facebook’s business. (Reporting by Alexei Oreskovic; Additional reporting by Doris Frankel in Chicago; Editing by Richard Chang and Lisa Shumaker)