The London Stock Exchange, which predates even its New York cousin by a century, is fighting harder in its bid to ward off a takeover effort by Nasdaq Stock Markets (NASDAQ:NDAQ). In doing so, it maintains that its newly released results for the quarter ended Dec. 31, 2006, indicate that the current Nasdaq offer significantly "undervalues the business."

The two trading entities have been jousting for nearly a year. Following a rejected bid for the LSE by Australia-based Macquarie Bank in December 2005, the Nasdaq emerged in March with its own offer for the exchange. When the latter offer was similarly rejected, the Nasdaq began acquiring a stake in the LSE, beginning with the 35.4 million shares owned by the largest LSE shareholder, Ameriprise Financial's (NYSE:AMP) Threadneedle Asset Management unit. Other smaller purchases have subsequently raised Nasdaq's stake to just less than 30%.

Despite intermittent cessations in its share purchases, as dictated by United Kingdom financial rules, Nasdaq revised its offer on Dec. 12, 2006. The U.S. exchange indicated that it would be able to complete the deal with slightly more than a 50% interest in the LSE, rather than the 90% it had been seeking.

On Tuesday, the LSE released the results for the third quarter of its 2007 fiscal year. Those results included a 53% rise in adjusted earnings to 39.1 pence a share year-to-date, following higher trading volumes and an increase in the number of companies listing on its markets.

In announcing its results, the exchange opined, "This excellent performance supports the board's rejection of Nasdaq's offer, which significantly undervalues the business and the Exchange's unique strategic position." Nasdaq's offer values the LSE at 2.7 billion pounds, or $5.2 billion. After the release of the exchange's third-quarter results, Nasdaq stated that it saw no reason to revise its offer and noted that it believes the LSE will face growing competition from investment banks, along with a commensurate need to cut its fees.

So the Nasdaq effort to wrest control of the London Exchange, the trading home of approximately 1,800 companies, appears no nearer a resolution than before. Indeed, British heels clearly are dug in, while the Nasdaq seems to be willing to avoid hasty escalations in its offer price in favor of slow, steady acquisitions of LSE shares until it reaches its magic "50% plus one share."

Parallel with the Nasdaq's efforts, U.S. investor Samuel Heyman said earlier this week that he had increased his own LSE stake to just less than 10%.

All of this is playing out amid investors' demands for increased globalization in their trading opportunities. As such, a takeover of the 300-year-old exchange seems ultimately inevitable, most likely by Nasdaq. At the same time, even the vaunted NYSE Group's (NYSE:NYX) New York Stock Exchange, founded under a buttonwood tree in lower Manhattan in 1792, will likely be forced to continue to dramatically change the way it conducts its own business, to bring itself into parity with the Nasdaq.

Indeed, the very nature of the auction market, with the specialist system as its vital cog, seems doomed to replacement. Once the auction market is gone completely, it'll probably be a good day for efficient investing, but a sad one for a venerable institution.

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Fool contributor David Lee Smith owns no shares in the companies mentioned. He welcomes your comments or questions.