Federal Reserve Chairman Ben Bernanke believes lawmakers have multiple options when it comes to replacing troubled mortgage giants Fannie Mae and Freddie Mac.

“There are a variety of organizational forms that might replace Fannie Mae and Freddie Mac that could likely provide mortgage credit without the systemic risks associated with these institutions in the past,” Bernanke said in a set of written responses to Rep. Marcy Kaptur (D., Ohio)  released Friday. Bernanke said overhaul of the housing finance system should focus on “accurate, transparent and risk-based pricing of government guarantees” and should create a system that provides a securitization market for mortgages, even in turbulent times.

What to do with the government-run firms is be one of the trickiest and most contentious issues facing Congress. Rep. Barney Frank (D., Mass.), chairman of the House Financial Services Committee, plans to start work on legislation this fall.

The U.S. took over Fannie and Freddie through a legal process known as conservatorship nearly two years ago and has pledged unlimited sums of aid the next three years to keep them afloat. So far, Fannie and Freddie have taken a combined $146 billion in injections from the Treasury.

But the firms are playing a major role in stabilizing the housing market. The two mortgage firms, along with the Federal Housing Administration, back more than 90 percent of new U.S. mortgages.