First Hawaiian Inc., the newly renamed subsidiary of French giant BNP Paribas, is seeking to raise up to $485 million in its initial public offering.

Hawaii’s largest bank said in a regulatory filing today that it is offering about 21.1 million shares of stock in a price range of $21 to $23 apiece. The amount raised could increase to as much as $557.8 million if an overallotment of an additional 3.2 million shares are purchased by underwriters of the deal.

All of the proceeds from the stock offering would be retained by BNP, which still would own at least 84.9 percent of the company. If the underwriters exercise their option to purchase the additional shares, BNP would own 82.6 percent of First Hawaiian.

First Hawaiian would have a market value of $3.2 billion based on 139.5 million outstanding shares if the stock is sold at the high end of the price range. Bank of Hawaii, the state’s second-largest bank, has a market capitalization of $3 billion based on today’s stock market close.

First Hawaiian would trade on the Nasdaq Global Select Market under the symbol FHB.

No date has been disclosed yet for the IPO although people with knowledge of the matter said last Friday that the offering would take place in the next couple of weeks.

First Hawaiian declined to comment.