The market for derivatives with payoffs contingent on the credit quality of a number of reference entities has grown considerably over recent years. The risk analysis and valuation of such multi-name structures often relies on simulating the performance of the underlying credits. In this paper we discuss the simulation of correlated unpredictable default arrival times. Our algorithm is based on the compensator of default. We construct this compensator explicitly in a multi-firm structural model with correlated defaults and imperfect asset and default threshold observation. It is shown how the model parameters can be estimated from readily available equity and single-name credit derivatives market data.