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Limit Theorems for Default Contagion and Systemic Risk

Hamed Amini 1 Zhongyuan Cao 2 Agnès Sulem 2 
2 MATHRISK - Mathematical Risk Handling
UPEM - Université Paris-Est Marne-la-Vallée, ENPC - École des Ponts ParisTech, Inria de Paris
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 di↵erent 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 di↵erent 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 di↵erent 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.
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Preprints, Working Papers, ...
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https://hal.inria.fr/hal-03429191
Contributor : Agnes Sulem Connect in order to contact the contributor
Submitted on : Monday, November 15, 2021 - 2:54:59 PM
Last modification on : Friday, November 18, 2022 - 9:25:23 AM
Long-term archiving on: : Wednesday, February 16, 2022 - 8:49:09 PM

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Hamed Amini, Zhongyuan Cao, Agnès Sulem. Limit Theorems for Default Contagion and Systemic Risk. 2021. ⟨hal-03429191⟩

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