Limit Theorems for Default Contagion and Systemic Risk

55 Pages Posted: 24 Mar 2021 Last revised: 15 Oct 2021

See all articles by Hamed Amini

Hamed Amini

Georgia State University

Zhongyuan Cao

INRIA Paris

Agnes Sulem

French National Institute for Research in Computer Science and Control (INRIA)

Date Written: March 24, 2021

Abstract


We consider a general tractable model for default contagion and systemic risk in a heterogeneous financial network, subject to an exogenous macroeconomic shock. We show that, under some regularity assumptions, the default cascade model could be transferred to a death process problem represented by balls-and-bins model. We also reduce the dimension of the problem by classifying banks according to different types, in an appropriate type space. These types may be calibrated to real-world data by using machine learning techniques. We then state various limit theorems regarding the final size of default cascade over different types. In particular, under suitable assumptions on the degree and threshold distributions, we show that the final size of default cascade has asymptotically Gaussian fluctuations. We next state limit theorems for different system-wide wealth aggregation functions and show how the systemic risk measure, in a given stress test scenario, could be related to the structure and heterogeneity of financial networks. We finally show how these results could be used by a social planner to optimally target interventions during a financial crisis, with a budget constraint and under partial information of the financial network.

Keywords: Systemic Risk, Default Contagion, Financial Networks, Limit Theorems.

JEL Classification: G01, G28

Suggested Citation

Amini, Hamed and Cao, Zhongyuan and Sulem, Agnes, Limit Theorems for Default Contagion and Systemic Risk (March 24, 2021). Available at SSRN: https://ssrn.com/abstract=3811107

Hamed Amini (Contact Author)

Georgia State University ( email )

Georgia State University
Atlanta, GA 30303
United States

Zhongyuan Cao

INRIA Paris ( email )

2 rue
Simone Iff
Paris, 75589
France

Agnes Sulem

French National Institute for Research in Computer Science and Control (INRIA) ( email )

40 avenue Halley
Villeneuve, 59650
France

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