BATS Trading, the alternative equity marketplace, moved to become a fully licensed securities exchange, filing an application with the U.S. Securities and Exchange Commission yesterday.

Joe Ratterman, BATS Chief Executive, said in a letter to subscribers and the trading community. that the “motivation to become an exchange is stems from our desire to participate directly in the national market system.”

The move could turn up the heat on Nasdaq and the New York Stock Exchange, as BATS ECN already has established itself as the third largest market center in the U.S. with a 6 percent to 8 percent matched market share in U.S. stocks.

“Is this the kind of exchange that you want as the viable alternative to the duopoly,” Ratterman asked in his letter to subscribers, encouraging them to review the exchange application once it is published for public comment.

BATS has been drafting its exchange application, which includes trading rules, governance and related exchange-member forms, since March of this eyar, Ratterman noted. Over the summer it made dozens of revisions and improvements to the application based on feedback from the SEC staff, he said.

If BATS were to become an exchange, it would gain “complete control over getting its own quote to the market, said a BATS Trading spokesman. “Currently we have to go through an exchange, (i.e., NSX and the International Securities Exchange), he notes.

Since it began operating in 2006, the BATS ECN has attracted broker dealers that do algorithmic or high frequency trading with is aggressive price rebates for liquidity providers. It also attracted investments from several leading brokers, including Citi, Credit Suisse, GETCO, Lime Brokerage Morgan Stanley, Merrill Lynch and Wedbush.

Volumes have grown from 59 million shares daily last October to more than 649 million shares in October 2007 when it recorded a one-day high of 774 million shares.