Correlated risks vs contagion in stochastic transition models

This paper studies the problem of disentangling risk correlation and contagion in a set of individual binary processes. The two admissible values correspond to bad and good risk states of an individual. The risk correlation is captured by introducing a dynamic frailty, whereas the contagion passes through the effect of the lagged number of individuals in the bad risk state. We study carefully the dynamic properties of the joint process. Then, we focus on the limiting case of large populations (portfolios). The difficulty to identify risk correlation and contagion in finite samples is illustrated by means of Monte-Carlo simulations.