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 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. The welfare benefits are quantitatively substantial: ARMs improve household welfare relative to FRMs by the equivalent of 0.83 percent of annual consumption under a monetary regime in which the central bank lowers real interest rates in a bust. Among designs that reduce payments in a bust, we show that those that front-load the payment reductions and concentrate them in recessions outperform designs that spread payment reductions over the life of the mortgage. 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 converted to an ARM with an FRM with an option to be refinanced at the prevailing FRM rate. Under these two contracts, the present value of a lender's loan falls by roughly an equal amount, as these contracts primarily differ in the timing of expected repayments. The FRM that can be converted to an ARM, which front loads payment reductions, improves household welfare by four times as much.