The question of listed exchanges (or "publicly traded exchanges") is now a live one in India. MCX seeks to do an IPO. A recent SEBI report says that regional stock exchanges should do IPOs and list on themselves. BSE could get listed, possibly on BSE.
I wrote an article in today's Business Standard titled Listed exchanges pose unique problems on this subject. I argue that exchanges are not ordinary firms, where we applaud when the firm graduates from startup to IPO. I suggest that listed exchanges pose daunting policy questions and that SEBI and MoF need to do deep thinking about whether India's interests are best served by a three-way separation between owners, managers and brokers.
I had blogged about the regional exchanges dimension earlier. I think the SEBI report on regional exchanges was wrong on notions of listing and possibly self-listing of regional exchanges.