The U.S. economy "feels good" and shows no sign of a recession in the next 12 months, Howard Lutnick, chairman and CEO of financial services company Cantor Fitzgerald, told CNBC on Monday.

"Everybody talks about this 'late cycle.' But they don't remember that this is easiest monetary policy in the history of modern finance," said Lutnick, who joined Cantor in 1983 armed with an economics degree. He became CEO in 1991 and then chairman as well in 1996. "This is just not your grandmother's economy."

The Federal Reserve's gradual tightening from zero percent interest rates — nine hikes since December 2015, four of which came last year, to a range of 2.25 percent to 2.50 percent — won't slam the lid on growth, Lutnick said.

"Sure it's getting a little bit harder, but it's still easy monetary policy," he contended. "So I think our economy has got a couple of years to run. I just don't see it coming to an end at the end of '19."

After the Fed's latest rate increase in December, central bankers were projected to hike twice this year. But on Jan. 4, Fed Chairman Jerome Powell said central bankers "will be patient" on rates given continued muted inflation.

Powell has "one in him" as far as rate hikes are concerned this year, said Lutnick, also chairman and CEO of BGC Partners, a brokerage that was spun off from Cantor in 2004. He added that Powell "will wait a little bit longer because the economy is bumpy" to pull the trigger again.

Still, Lutnick sees sustained economic growth in the mid-2 percent range going forward after a stronger 2018 for gross domestic product, including advances of 2.2 percent in the first quarter, 4.2 percent in the second quarter, 3.4 percent in the third quarter, and estimates of around 3 percent for the fourth quarter.

Meanwhile, the cut in the corporate tax rate from 35 percent to 21 percent will give a lasting boost to the economy, Lutnick said. "You have like trillions of dollars in Europe, forced to be in Europe ... you think it's all back? There's not a chance it's all back." There's been a debate on whether companies that have brought money back have used it to invest in their businesses or whether they've sought to boost their stocks through share buybacks.

Lutnick is known for rebuilding Cantor after the Sept. 11, 2001, World Trade Center terrorist attacks. The company lost more than two-thirds of its then-960 New York-based employees, including Lutnick's brother. Cantor and its affiliates now have more than 4,000 employees in New York and more than 10,000 globally.