One of the investment firms pressuring Corrections Corp. of America to convert to a real estate investment trust has increased its stake in the prison manager by exercising a big batch of stock options.

New York-based Corvex Management has filed papers with the Securities and Exchange Commission detailing its option move, which was completed Friday. The money manager, which controls about $1 billion for its investors, paid $18 to exercise almost 2.3 million shares. That lifted the stake held by Corvex and San Francisco-based Marcato Capital to 7.6 percent, behind only Lazard Asset Management's 8.8 percent.

Corvex and Marcato in April called on CCA's board to look into converting to REIT status, saying it would lower the company's capital costs and boost its stock valuation. Early this month, CCA officials said they have in fact been studying the REIT option since late 2011.

Shares of CCA (Ticker: CXW) were trading up 1 percent at $26.26 early Monday afternoon. Year to date, they're up almost 30 percent but are off about 3 percent since Corvex/Marcato's appeal to convert to a REIT.