"We've been very successful since 2008 actually not entering into derivatives, not doing any hedging," Parker said in an interview on CNBC's "Squawk Box."
"The fuel price this year versus last year at today's prices and today's forward curves [is] about $4.5 billion lower than what we paid last year," he said. "So that certainly helps out earnings [in 2015]."
But that won't mean lower air fares, Parker said, because the drop in crude is supply-driven and "demand for air travel remains very strong."
American Airlines Group is the holding company for American Airlines and US Airways, which completed their merger in December 2013.
After the close of trading on March 20, the company to the index, which Parker said happened sooner than expected. He said it's good for American and its shareholders.
In 2014, investors in American Airlines saw strong earnings growth, and in the past 12 months a stock that was up nearly 40 percent as of Monday's closing price. Business for American and the industry as a whole is expected to remain brisk. In fact, according an estimate last week from the trade group Airlines for America, U.S. carriers are seen having their best spring in seven years.
Parker was in Washington, D.C., for the Chamber of Commerce Foundation's annual Aviation Summit, where American, Delta, United Continental and the airline unions are going to plead their case for fair competition.
A new white paper—released by the airlines and their labor organizations—claims Qatar Airways, Etihad Airways and Emirates have received $42 billion in quantifiable subsidies and other unfair benefits from their respective governments in direct violation of U.S. Open Skies policy.
The Open Skies agreements with partner countries seek to set a level playing field, free of "government interference in commercial airline decisions," according to the State Department. Such deals with Qatar and the United Arab Emirates were signed in 2001 and 2002, respectively.
"We don't believe it's fair trade," Parker said. "All we're asking is that we have a conference about this, consultations, to talk with those governments and our government … to have them enforced."
Emirates, Qatar Airways and Etihad , saying U.S. airlines have lost market share because of their inferior service.