Getty Images People wait in line at a cashless exchange desk during the Euro 2016 soccer tournament.There’s nothing quite like a $10 billion deal to bring excitement to a sector. U.S. payments processor Vantiv’s VNTV, +0.39% announcement this month that it plans to pay that amount for British rival Worldpay Group WPG, +0.16% triggered a fresh burst of chatter about the relentless shift away from cash to cards and digital transfers—and raised the profile of payments processors. “The disappearance of cash and checks is the main driver,” says Richard-Maxime Beaudoux, a Paris-based senior equity research analyst at investment bank Bryan, Garnier & Co. Global noncash transactions jumped by 11% to $433 billion in 2015, the most recent data available, and more strong growth is ahead, according to Capgemini, the consulting giant. A second key driver for the payment services sector is e-commerce ramping up worldwide, says Beaudoux—and another is a steady stream of mergers and acquisitions. But investors may want to wait for the recent excitement to die down. European stocks in the sector seem a bit pricey after this month’s rally on deal news, which included a $3.8 billion bid for British card processor Paysafe Group PAYS, -0.17% that came to light Friday.via