Abstract
We offer a stress test framework in which interaction between regulated banks occurs through the impact they may have on asset prices when they deleverage. Because banks are constrained to maintain their risk-based capital ratio higher than a threshold, the deleveraging problem yields a generalized game in which the solvency constraint of each bank depends on the decisions of the others. We analyze the game under microprudential but also under macroprudential regulation. Microprudential regulation corresponds to the standard situation in which each bank considers its own solvency constraint, whereas macroprudential regulation is defined as the situation in which each bank faces a systemic constraint in that it must consider the solvency constraints of all the banks. When bankruptcies can be avoided, we show that a Nash equilibrium generically exists under macroprudential regulation, contagion of failures due to fire sales externalities is prevented, whereas it may not exist under microprudential regulation. We eventually analyze the deleveraging problem when bankruptcies cannot be avoided and present additional results.
