A widening probe of the foreign-exchange market is roiling an industry already under pressure to reduce costs as computer platforms displace human traders.

Electronic dealing, which accounted for 66 percent of all currency transactions in 2013 and 20 percent in 2001, will increase to 76 percent within five years, according to Aite Group LLC, a Boston-based consulting firm that reviewed Bank for International Settlements data. About 81 percent of spot trading—the buying and selling of currency for immediate delivery—will be electronic by 2018, Aite said.

“Foreign-exchange traders are much like stock floor traders: a rapidly dying breed,” said Charles Geisst, author of “Wall Street: A History” and a finance professor at Manhattan College in Riverdale, New York. “Once the banks realize they are costing them money, the positions will dwindle quickly.”