Shares of real estate services provider Realogy, whose brands include Century 21, Coldwell Banker and The Corcoran Group, soared more than 25 percent in their first day of trading on the New York Stock Exchange.

The company’s stock jumped $7.20 to $34.20 on Thursday. It opened at $32.85.

Realogy Holdings said its IPO of 40 million shares priced at $27 per share, at the high end of the projected range of $23 to $27 per share.

The Parsippany, N.J., company, whose other brands include ERA and Sotheby’s International Realty, raised $1.08 billion from the offering. That makes it the third-largest U.S. IPO of the year, according to Renaissance Capital.

Realogy plans to use the proceeds it receives from the IPO, along with available cash, mostly to pay down debts. The company’s total debt was approximately $7.34 billion as of June 30.

After the market closed Thursday, the rating agency Standard & Poor’s raised Realogy’s credit grade one notch, from CCC to B, citing the company’s plans to pay off roughly $1 billion in outstanding debts.

Realogy, which is controlled by private equity firm Apollo Global Management, said in a filing with the Securities and Exchange Commission that it believes the residential real estate market is in the beginning of a recovery. The company said it sold 13 percent more homes during the first eight months of the year, compared with the same span in 2011.

Signs of a recovery are a welcome sight for Realogy, which saw its revenue drop $2.4 billion from 2006 through 2011 as the housing market faltered. The company said it worked during those lean years to reduce costs, which included making job cuts and consolidating or closing offices.

Realogy had about 15,000 employees at the beginning of 2006. By the end of 2011, it was down to approximately 10,400. The company also consolidated or closed 358 brokerage offices during that time.

Like many companies working their way back from the damage that the recession and housing market downturn inflicted, Realogy still needs to improve its financial performance. The company’s loss widened in 2011 mostly on high interest expense obligations, while its revenue was basically flat at $4.09 billion.

It is giving the underwriters a 30-day option to buy up to an additional 6 million shares, less underwriting discounts and commissions.

Realogy’s stock is trading under the “RLGY” ticker symbol.