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Limit Theorems for Default Contagion and Systemic Risk

Author

Listed:
  • Hamed Amini

    (Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611)

  • Zhongyuan Cao

    (INRIA Paris, MathRisk Project Team, 75589 Paris Cedex 12, France; Université Paris-Dauphine, CEREMADE, 75775 Paris Cedex 16, France)

  • Agnès Sulem

    (INRIA Paris, MathRisk Project Team, 75589 Paris Cedex 12, France)

Abstract

We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network subjected to an exogenous macroeconomic shock. We show that under certain regularity assumptions, the default cascade model can be transformed into a death process problem represented by a balls-and-bins model. We state various limit theorems regarding the final size of default cascades. Under appropriate assumptions on the degree and threshold distributions, we prove that the final sizes of default cascades have asymptotically Gaussian fluctuations. We next state limit theorems for different system-wide wealth aggregation functions, which enable us to provide systemic risk measures in relation to the structure and heterogeneity of the financial network. Lastly, we demonstrate how these results can be utilized by a social planner to optimally target interventions during a financial crisis given a budget constraint and under partial information of the financial network.

Suggested Citation

  • Hamed Amini & Zhongyuan Cao & Agnès Sulem, 2024. "Limit Theorems for Default Contagion and Systemic Risk," Mathematics of Operations Research, INFORMS, vol. 49(4), pages 2652-2683, November.
    • Handle: RePEc:inm:ormoor:v:49:y:2024:i:4:p:2652-2683
    DOI: 10.1287/moor.2021.0283
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