First Internet Bancorp, parent of Indianapolis-based First Internet Bank of Indiana, is seeking to have its stock traded on the NASDAQ exchange.

The company announced Tuesday that it has filed with the Securities and Exchange Commission to make the move from the over-the-counter board.

Company shares, which opened Wednesday morning priced at $19.25 each, have been listed on the thinly traded OTC market under the FIBP ticker symbol since 2005.

Chairman and CEO David Becker said in a prepared statement that he expects the change to be completed sometime next year.

“The board of directors believes that our plan to move from the over-the-counter market to a national exchange will enhance the trading market for our stock and provide a long-term benefit to our shareholders,” he said.

Becker founded First Internet Bank in 1999. The bank has no branches and has 95 employees at its corporate headquarters at 9200 Keystone Crossing. First Internet said in its SEC filing that it expects to move early next year into 23,891 square feet of space, which is more than 9,000 square feet larger than its current office.

For the quarter ended Sept. 30, the company earned $1.6 million, or 85 cents per share, compared with $765,000, or 40 cents per share, during the same period last year.

Through the first nine months of 2012, the bank reported profit of $4 million, or $2.12 per share, compared with $2.1 million, or $1.12 per share, in the year-ago period.

First Internet attributed the increase to gains on loans sold and growth in deposits.

Loans held for sale totaled $55.5 million as of Sept. 30, compared with $44.4 million at the same time in 2011.

Total deposits in the third quarter grew 13 percent, to $522.7 million.

Assets increased 12 percent, to a record $627.7 million.

On Nov. 20, the bank announced a cash dividend of 25 cents per share payable Dec. 28, the first dividend the bank has ever paid.