We incorporate house price risk and mortgages into a standard incomplete market (SIM) model. We calibrate the model to match U.S. data, and we show that the model also accounts for non-targeted features of the data such as the distribution of down payments, the life-cycle profile of homeownership, and the mortgage default rate. In addition, we show that the average coefficients that measure the agents' ability to self-insure against income shocks are similar to those of a SIM model without housing (as presented by Kaplan and Violante, 2010). However, incorporating housing increases the values of these coefficients for younger agents, which narrows the gap between the SIM model's implications and the data. The response of consumption to house price shocks is minimal. We also study the effects of default prevention policies. Introducing a minimum down payment requirement of 15 percent reduces defaults on mortgages by 30 percent, reduces the homeownership rate up to only 0.2 percentage points (if the aggregate house price level does not adjust), and may cause house prices to decline up to 0.7 percent (if homeownership does not adjust). Garnishing defaulters' income in excess of 43 percent of median consumption for one year produces a similar decline in defaults; but, since it reduces the median equilibrium down payment from 19 percent to 9 percent, it boosts homeownership up to 4.3 percentage points (if the aggregate house price level does not adjust) and may increase house prices up to 16.1 percent (if homeownership does not adjust). The introduction of minimum down payments or income garnishment benefit a majority of the population.