Paper: arXiv 2601.01505

Authors: Marco Ioffredi, Stefano Marmi, Matteo Tanzi

Abstract

Systemic financial risk refers to the simultaneous failure or destabilization of multiple financial institutions, often triggered by contagion mechanisms or common exposures to shocks. In this paper, we present a dynamical model of bank leverage (the ratio of asset holdings to equity) a quantity that both reflects and drives risk dynamics. We model how banks, constrained by Value-at-Risk (VaR) regulations, adjust their leverage in response to changes in the price of a single asset, assumed to be held in fixed proportion across banks. This leverage-targeting behavior introduces a procyclical feedback loop between asset prices and leverage. In the dynamics, this can manifest as logistic-like behavior with a rich bifurcation structure across model parameters. By analyzing these coupled dynamics in both isolated and interconnected bank models, we outline a framework for understanding how systemic risk can emerge from seemingly rational micro-level behavior.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework utilizing coupled unimodal maps and dynamical systems theory to study systemic leverage synchronization. However, it is purely theoretical and lacks empirical validation or backtesting on real-world financial data.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Systemic Financial Risk via Bank Leverage Dynamics] --> B[Model Inputs: Single Asset Price, Fixed Equity, VaR Constraints]
    B --> C[Micro-Level Modeling: Unimodal/Logistic Maps for Procyclical Leverage Targeting]
    C --> D[System Coupling: Connect Isolated Banks via Shared Asset Exposure]
    D --> E[Computational Process: Bifurcation Analysis & Chaos/Synchronization Simulations]
    E --> F[Key Outcomes: Rational Micro-Behavior Drives Chaos, Synchronization & Systemic Failure]

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