As the largest U.S. banks rebuild their mortgage lending, with gains last quarter, they face the challenge of finding qualified borrowers and the possibility of rising interest rates.

JPMorgan Chase & Co., Wells Fargo & Co. and Citigroup Inc. all posted mortgage lending gains in the third quarter from the prior period, according to statements yesterday. Refinancing by homeowners, who took advantage of the lowest interest rates of the year, drove the industry’s growth, according to an estimate by the Mortgage Bankers Association (MBA).