Abstract:

We consider heterogeneous grouping cases where parameters are identical within their own groups but different between groups. Given this heterogeneity, a central bank has to keep deposits or provide extra cash flow instead of acting as a clearing house and systemic risk happens in the more complicated manner than the homogeneous case. In addition, in order to prevent systemic risk, a central bank must take control of the ensemble average. Instead of acting a scaled Brownian motion, the ensemble average can be driven by the Ornstein-Uhlenbeck process through the control given by a central bank leading to the smaller probability of the large number of defaults.