World capital markets have experienced large-scale sovereign defaults on a number of occasions, the most recent being Argentina's default in 2002. In this paper, we develop a quantitative model of debt and default in a small open economy. We use this model to match four empirical regularities regarding emerging markets: defaults occur in equilibrium, interest rates are countercyclical, net exports are countercyclical, and interest rates and the current account are positively correlated. That is, emerging markets on average borrow more in good times and at lower interest rates than in slumps. Our ability to match these facts within the framework of an otherwise standard business-cycle model with endogenous default relies on the importance of a stochastic trend in emerging markets.