Playing with Fire? A Mean Field Game Analysis of Fire Sales and Systemic Risk under Regulatory Capital Constraints

Abstract: We study the impact of regulatory capital constraints on fire sales and financial stability in a large banking system using a mean field game model. In our model banks adjust their holdings of a risky asset via trading strategies with finite trading rate in order to maximize expected profits. Moreover, a bank is liquidated if it violates a stylized regulatory capital constraint. We assume that the drift of the asset value is affected by the average change in the position of the banks in the system. This creates strategic interaction between the trading behavior of banks and thus leads to a game. The equilibria of this game are characterized by a system of coupled PDEs. We solve this system explicitly for a test case without regulatory constraints and numerically for the regulated case. We find that capital constraints can lead to a systemic crisis where a substantial proportion of the banking system defaults simultaneously. Moreover, we discuss proposals from the literature on macroprudential regulation. In particular, we show that in our setup a systemic crisis does not arise if the banking system is sufficiently well capitalized or if improved mechanisms for the resolution of banks violating the risk capital constraints are in place.