In this paper, we solve a dynamic model of households' mortgage decisions incorporating labor income, house price, inflation, and interest rate risk. Using a zero‐profit condition for mortgage lenders, we solve for equilibrium mortgage rates given borrower characteristics and optimal decisions. The model quantifies the effects of adjustable versus fixed mortgage rates, loan‐to‐value ratios, and mortgage affordability measures on mortgage premia and default. Mortgage selection by heterogeneous borrowers helps explain the higher default rates on adjustable‐rate mortgages during the recent U.S. housing downturn, and the variation in mortgage premia with the level of interest rates.

The benefits of endowment destruction documented by Ljungqvist and Uhlig (2015), and the related possibility that consumption can lower habits, are fragile. Both issues result from a particular way of discretely approximating the underlying continuous-time model or of adapting it to jumps. Other ways of calculating the discrete-time approximation or extending the model to jumps easily overturn the results, while making no difference to the model's description of asset prices and quantities. This analysis gives an example of how to extend models so that the jump gives the same result as a jump limit of continuous-sample-path movements.