How can mortgages be redesigned to reduce housing market volatility, consumption volatility, and default? How does mortgage design interact with monetary policy? We answer these questions using a quantitative equilibrium life cycle model with aggregate shocks, long-term mortgages, and an equilibrium housing market, focusing in particular on designs that index payments to monetary policy. Designs that raise mortgage payments in booms and lower them in recessions do better than designs with fixed mortgage payments for insurance and risk reasons. The welfare benefits are quantitatively substantial: ARMs improve household welfare relative to FRMs by the equivalent of 1.00 percent of annual consumption if the central bank lowers interest rates in a bust. Among designs that reduce payments in a bust, we show that those that front-load the payment reductions, concentrating them in the recession, rather than spreading payment reductions over the life of the mortgage perform best. This is the case because front- loading alleviates household liquidity constraints in states where they are most binding, reducing default and stimulating housing demand by new homeowners. To isolate this channel, we compare an FRM with a built-in option to be costlessly converted to an ARM with an FRM with an option to be costlessly refinanced at the prevailing FRM rate. Under these two contracts, lenders experience roughly equal losses in a crisis as they are indifferent to their position on the equilibrium yield curve, but the FRM convertible to the ARM improves household welfare by three times as much.