First Hawaiian Bank’s parent company ended up raising more than $550 million in its initial public offering.

The holding company for the state’s largest bank said Tuesday that underwriters have fully exercised their option to purchase an additional 3.2 million shares at the offering price of $23.

First Hawaiian’s stock closed Tuesday down 17 cents at $24.41 on the Nasdaq.

The sale of the additional shares brings the total number of shares pur-chased in the offering to 24.25 million and increases the amount raised to $557.8 million.

The additional shares sold also reduced BNP Paribas’ stake in First Hawaiian Inc. to 82.6 percent from 84.9 percent.

Goldman, Sachs & Co., BofA Merrill Lynch and BNP Paribas were the primary underwriters.

BNP, which previously owned 100 percent of First Hawaiian, keeps all the money raised from the IPO pricing. The Paris-based bank said it needed to sell off part of its stake to generate more capital and satisfy regulatory requirements. BNP has said in Securities and Exchange Commission filings that it plans to sell off its remaining ownership of the bank over an unspecified period of time.

The stock ended its first day of trading Thursday up $1.25 at $24.25 and then rose to $24.84 Friday. But the stock has since lost ground the first two trading days of this week, falling to $24.58, down 26 cents, Monday and then slipping again Tuesday.

Volume has fallen each day of trading after 11.7 million shares exchanged hands on its IPO. The volume Tuesday was 688,038 shares.

First Hawaiian’s market capitalization of $3.40 billion still ranks first in the state among publicly traded companies. Hawaiian Electric Industries Inc. is close behind with a value of $3.31 billion, and Bank of Hawaii Corp. is next at $3.01 billion. The market cap is determined by multiplying the company’s stock price by its number of outstanding shares.

The IPO was the largest for a U.S. bank since Citizens Financial Group Inc. raised $3.5 billion in 2014.