Brad Katsuyama and Bill O'Brien CNBC screenshot Two CEOs of exchanges got in a nasty brawl on CNBC's "Power Lunch" over high-frequency trading.

William "Bill" O'Brien, the CEO of BATS, slammed Brad Katsuyama, the CEO and president of IEX, and author Michael Lewis.

Katsuyama is the hero in Michael Lewis' new book, "Flash Boys." His firm, IEX, is an alternative exchange.

"I've been shaking my head a lot quite frankly the last 36 hours ... Michael and Brad, shame on both of you," he said, adding that they've possibly scared "millions of investors in an effort to promote a business model."

CNBC correspondent Bob Pisani asked Katsuyama if he thought the markets were rigged.

"I think it's really hard to put a word on it," Katsuyama began.

O'Brien jumped in. "He said it in the book. You said it in the book ... it's disgusting that you're trying to parse your words now. You can't say that ... Do you believe it or not? Because you said it."

"I believe the markets are rigged. And I also think that you're a part of the rigging. So if you want to do this, let's do this," Katsuyama said.

Katsuyama said that it's the responsibility of a venue to fairly price trades between fast and slow participants.

The brokers on the floor of the New York Stock Exchange exploded with cheers at this comment.

"You had a 300-page commercial, OK? So let me talk," O'Brien shot back later in the interview, referring to Lewis' new book.

During the interview, Katsuyama said he thought we should get rid of the term "high-frequency trading."

"You used it 20 times in your book!" O'Brien said.

"It's not his book," CNBC anchor Tyler Mathisen jumped in before they brought Michael Lewis back into the discussion.

"I've been enjoying that," Lewis said. "It's great to see Bill ... tell Brad he's doing this to promote a business model." He added that O'Brien was saying "shame on you" to Katsuyama.

"I'll say it again," O'Brien shot back.

"I think he's outrageous. I think he's part of the problem," Lewis told CNBC.

O'Brien then accused Lewis of never visiting BATS. Lewis said he toured the place on Feb. 5, 2013.

"OK, we are going to follow up with CNBC about where Michael Lewis was on Feb. 5, 2013," O'Brien said.

He asked if he was in Kansas City. "That's where we're located, by the way!"

"There's actually no point in talking to someone who's just throwing dust in the air," Lewis said of O'Brien, pointing out that he wasn't the head of BATS when he wrote about the stuff that occurred.

Lewis said he was curious if they put the exchange on the other side of the Lincoln Tunnel intentionally in an effort to pick off orders.

O'Brien told Lewis his book was "riddled with inaccuracies."

"You can get on air and shout all you want," Lewis said, "But it's just not true."

"You have a much bigger soapbox than I do," O'Brien said.