A model describing an economy where companies may default due to contagion is proposed in this paper. By using standard approximation results for stochastic processes, we are able to describe the features of the model. It turns out that the model reproduces the oscillations in the default rates that have been observed empirically. That is, we have an intrinsic oscillation in the economic system without applying any external macroeconomic force. These oscillations can be understood as a cleansing of the unhealthy companies during a recession, and as the recession ending when a sufficient number of the unhealthy companies have left the economy. This is important both from a risk management perspective and a policy perspective, since it shows that contagious defaults may help to explain the oscillations of business cycles. We also investigate the first-passage times of the default process, using this as a proxy for the time until a recession.