Correlated Risks vs Contagion in Stochastic Transition Models

There is a growing literature on the possibility to identify correlation and contagion in qualitative risk analysis. Our paper considers this question by means of a model describing the joint dynamics of a set of individual binary processes. The two admissible values correspond to bad and good risk states of an individual. The risk correlation and its time dependence are 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) and reconcile the microscopic and macroscopic dynamic views of the risk. The difficulty to identify in finite sample risk correlation and contagion is illustrated by means of Monte-Carlo simulations