After CME Group Inc (NASDAQ:CME) said earlier this week it had no plans to go private at this time, an exchange across town had a different answer: yes if it benefits its shareholders.?

CBOE’s President and Chief Operating Officer Edward Tilly, also speaking at the same Credit Suisse financial services forum, said on the subject via Reuters, “We still must act and are looking forward to acting in the best interest of our stockholders. If valuations as a result of conversations with Carlyle lift all boats, so be it; We would have to entertain changes in our structure.”

This comes after it was disclosed this week that the private equity firm Carlyle Group and ?Nasdaq OMX Group Inc held discussions about possibly taking the exchange private. Since then, it’s been a topic of conversation for the exchanges and the question has been posed to a few on whether they would do so. ?

For CBOE, it just lost its private status in 2010 after years of battling to make the change to a public company. Tilly will take over the exchange’s reins in May when current?CBOE Chief Executive Bill Brodsky steps down.

But for now, being a public company is o.k. Tilly added, “We are getting into a nice rhythm as a public company.”

The market appeared to like Tilly’s comments about going private. CBOE’s stock is currently trading at $35.82, up ?2.37%–a record high for the shares.