The rivals vying to control NYSE Euronext are full of bravado when it comes to predicting their chances of winning the approval of U.S. and European regulators. But the bluster isn't backed up by a clear picture of how either deal gets the assent.

Indeed, both deals will likely require significant divestitures to win approval.

That unhappy fact runs counter to optimistic projections coming from both sides. While executives acknowledge that winning antitrust clearance will be a lengthy process, they insist any conditions will be relatively painless. It's the other guy who's heading to perdition.

NYSE Euronext officials reiterated that view April 21 when the board again rejected the $11.3 billion bid from Nasdaq OMX Group Inc. and IntercontinentalExchange Inc. to stick with the $10.2 billion deal with Deutsche Börse AG. The Nasdaq-ICE bid, they insist, faces nearly insurmountable obstacles to winning clearance from the Department of Justice. "This proposal does not provide compelling value, has unacceptable execution risk and is therefore not in the best interests of NYSE Euronext shareholders," NYSE Euronext chairman Jan-Michiel Hessels said in a statement. The highest hurdle, NYSE and Deutsche Börse officials say, is that Nasdaq and NYSE dominate listings of public companies in the U.S., and together would create a monopoly.

But the Deutsche Börse bid has its own problems. Several analysts say NYSE Euronext's Liffe derivatives unit, which, combined with Deutsche Börse's Eurex, would dominate derivatives in Europe, is likely to be ordered sold by the European Commission. "I think both deals have risk, there's no question about it. On our side it's obvious ... we have a lot of work to do with the competition authorities in Brussels, to talk about the derivatives market and OTC derivatives market," NYSE Euronext chief executive Duncan Niederauer said on CNBC April 11. Combining the two companies' derivative platforms was a major reason for the deal.

The most likely scenario for the Nasdaq deal -- outside of DOJ rejection -- is an order to divest the American Stock Exchange, which NYSE acquired in 2008. A spinoff of Amex would create another listings venue. NYSE and Deutsche Börse execs have been tight-lipped about their strategy, but they are likely to argue that an Amex spinoff is unnecessary because Bats Global Markets Inc. plans to launch a U.S. listing service this summer. Observers, however, say the DOJ is likely to be skeptical that either startup Bats or long-declining Amex will be sufficient listing competitors.

Options also pose a problems for the Nasdaq offer. NYSE Arca Options and NYSE Amex Options combined with Nasdaq OMX PHLX and the Nasdaq Options Market would have a 55% market share. There are six rivals in U.S. options, but two, the Boston Options Exchange Group LLC and Bats, have tiny shares. If the DOJ ignored the two smaller operations, the merger would shrink the number of options competitors from four to three, a level of concentration it typically frowns upon.

Like their rivals, Nasdaq and ICE have insisted their bid is likelier to gain favor. "The substantial overlap in the Deutsche Börse and NYSE Euronext European derivatives businesses may create execution and timing risk in the Deutsche Börse deal," Nasdaq CEO Robert Greifeld wrote in an April 19 letter to the NYSE board offering a $350 million breakup fee if the Nasdaq bid fails to gain regulatory approval. "Our addition of a reverse break-up fee demonstrates our confidence."

But Nasdaq and ICE have been unusually up front about their negotiating strategy with regulators.

ICE CEO Jeffrey Sprecher laid out for analysts in an April 20 conference call how the companies plan to make their case. The main goal will be to convince regulators that the bid would preserve competition in more sectors. "We believe there's a great deal of opportunity to be had by keeping Liffe as a nimble competitor to Deutsche Börse and to [CME Group Inc.] rather than make it part of a smaller monopoly derivatives exchange that has yet to carve out a toehold in the over-the-counter market," he said.

Although Liffe has been a minor rival so far, he said "our combination would be a significant and strong competitor to both the Deutsche Börse and the CME."

As far as concerns about concentration in U.S. listings, Greifeld told analysts there should be no worries about new competitors entering the business. Private trading, he added, also offers an alternative to public listings. He insisted the listing market is a global one with many competitors.

He noted that while he was visiting with the DOJ, Glencore International AG announced it would list on two non-U.S. exchanges. "We have a Swiss company listing in Hong Kong and London." That such a listing once would have been made in the U.S. is "helpful" to Nasdaq's argument that its bid will create a stronger global competitor.

Smaller listings rivals, he argued, can enter on the cheap. He said Nasdaq has spent two years trying to get Securities and Exchange Commission approval for a "quasi-venture" market approved. Once Nasdaq's application sets the precedent, rivals like Bats and Direct Edge Holdings LLC can get their own applications approved.

It may take such a novel argument for either deal to pass with regulators.