How much of the recent rise in foreclosures can be explained by the large number of nontraditional, low-downpayment mortgage contracts originated between 2003 and 2006? We present a model where heterogeneous households select from a set of possible mortgage contracts and choose whether to default on their payments given realizations of income and housing price shocks. The set of contracts consists of traditional fixed rate mortgages as well as nontraditional mortgages with low downpayments and delayed amortization schedules. The mortgage market is competitive and each contract, contingent on household earnings and assets at origination as well as loan size, must earn zero expected profits. In this model, an unanticipated 25% housing price decline following a brief introduction of non-traditional mortgages causes an increase in foreclosure rates that closely approximates the 150% increase in the data between the first quarter of 2007 and the first quarter of 2009. The model also matches origination rates for nontraditional mortgages observed prior to the crisis. Since we do not select parameters to match these two key aspects of the recent data, these quantitative predictions provide support for our model. In a counterfactual experiment where new mortgages are not introduced, the same price shock causes foreclosure rates to increase by only 86%. Thus, the availability and popularity of nontraditional mortgages in the four years prior to the crisis can explain over 40% of the rise in foreclosures.