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A framework for analyzing contagion in assortative banking networks.

Thomas R Hurd1, James P Gleeson2, Sergey Melnik2

  • 1Department of Mathematics, McMaster University, Hamilton, Ontario, Canada.

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This study introduces a new framework to predict financial contagion, analyzing how bank network structures influence systemic risk. It proposes a cascade condition to measure risk, finding that assortativity significantly impacts contagion spread.

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Area of Science:

  • Financial network analysis
  • Systemic risk modeling
  • Complex systems

Background:

  • Previous models of financial networks often assume independent bank connections.
  • Understanding contagion dynamics in banking systems is crucial for financial stability.
  • Stylized banking network representations lack the ability to model specific connection preferences.

Purpose of the Study:

  • To develop a probabilistic framework for predicting contagion event sizes in stylized banking networks.
  • To explicitly incorporate (dis)assortative edge probabilities into financial network models.
  • To derive a quantifiable measure of systemic risk based on network topology.

Main Methods:

  • Developed a probabilistic framework for stylized banking networks.
  • Analyzed default cascades using iterated mappings on edge probabilities.
  • Derived a cascade condition analogous to R0 in epidemic modeling.
  • Applied percolation theory to random networks to determine global cascade frequency.
  • Utilized Monte Carlo simulations for finite-sized networks.

Main Results:

  • A cascade condition was derived, indicating the potential for systemic risk propagation.
  • Analytical results showed limited quantitative agreement with simulations.
  • Edge-assortativity was found to significantly affect systemic risk levels.
  • A graph-assortativity coefficient was proposed to assess systemic risk.

Conclusions:

  • The proposed framework allows for predicting contagion event sizes by considering network structure.
  • The cascade condition provides an accessible measure of systemic risk.
  • Assortativity's subtle but strong influence on systemic risk is highlighted, with a new metric proposed for its assessment.