Paper: arXiv 2406.17528

Authors: Rüdiger Frey, Theresa Traxler

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical Mean Field Game of Controls (MFGC) framework using coupled forward-backward PDEs to model fire sales under regulatory constraints. However, it relies entirely on numerical simulation and synthetic test cases rather than empirical financial data backtesting.

Research Flowchart

  flowchart TD
    A["Research Goal: Analyze Capital Constraints,<br>Fire Sales & Systemic Risk"] --> B["Data/Inputs: Banking System Parameters,<br>Trading Rates & Capital Rules"]
    B --> C["Methodology: Mean Field Game Model<br>with Asset Drift Interaction"]
    C --> D["Mathematical Formulation:<br>Coupled System of PDEs"]
    D --> E["Computation: Explicit Solution (Unregulated)<br>vs. Numerical Solver (Regulated)"]
    E --> F["Key Findings: Tight Constraints Cause Systemic Crises;<br>High Capital & Better Resolution Prevent Cascades"]

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