We examine multi-name credit models from the perspective of point processes. In this context, it is natural to pursue a top down approach: the economy as a whole is modeled first. The technique of random thinning consistently generates sub-models for individual firms or portfolios. A candidate for the top down approach is a self-exciting process, whose intensity at any time depends on the sequence of events observed up to that time. A self-exciting process incorporates the contagion observed in

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... credit markets and avoids an ad hoc choice of copula. The familiar doubly stochastic process is at the opposite end of the spectrum in the sense that it is constructed from the bottom up: individual firm intensities are estimated and then aggregated. We rigorously analyze self-exciting and doubly stochastic processes with respect to their ability to capture contagion. Model fitness can be tested using a deep result of Meyer (1971), which shows that any point process with continuous compensator can be transformed into a standard Poisson process by a change of time. Meyer's result allows us to extend the scope of the tests proposed by Das, Duffie & Kapadia (2004) for a doubly stochastic model.