Shares jumped close to 7 percent Tuesday, reaching an intraday high of $52.58. It had jumped 73 percent on its first day of trading, but simmered down thereafter, falling to a low of $38.80.
This compares with $50.09 the day it went public, and comes off as bizarre as most analysts maintain "buy" or "hold" ratings or the stock, considering it overvalued.
Increased investor confidence could come from the release of a new advertising product on Thursday, which investors hope could help make Twitter a profitable company at last. The product, called Tailored Audiences, will help push more relevant ads to user feeds.
Twitter advertising's value became more apparent after National Geographic revealed success Monday on Twitter-aided TV ad campaigns for Killing Kennedy.
But the surge could also come from a Wall Street rumor that Carl Icahn, the activist investor known for pressuring companies such as Apple, Dell and Transocean, may have bought a stake in the company.
Also Twitter, along with a number of other technology giants like Google, Apple, Facebook and LinkedIn, is said to have its profit motives in mind when pressuring the U.S. government to revamp the National Security Agency's snooping habits.
The volatile Twitter stock compares with Facebook, which took more than a year to break through to a new high after its first day of trading. And LinkedIn, which started trading at $45 rallied between $60 and $100 in just months of trading.