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Systemic Cascades On Inhomogeneous Random Financial Networks

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  • T. R. Hurd

Abstract

This systemic risk paper introduces inhomogeneous random financial networks (IRFNs). Such models are intended to describe parts, or the entirety, of a highly heterogeneous network of banks and their interconnections, in the global financial system. Both the balance sheets and the stylized crisis behaviour of banks are ingredients of the network model. A systemic crisis is pictured as triggered by a shock to banks' balance sheets, which then leads to the propagation of damaging shocks and the potential for amplification of the crisis, ending with the system in a cascade equilibrium. Under some conditions the model has ``locally tree-like independence (LTI)'', where a general percolation theoretic argument leads to an analytic fixed point equation describing the cascade equilibrium when the number of banks $N$ in the system is taken to infinity. This paper focusses on mathematical properties of the framework in the context of Eisenberg-Noe solvency cascades generalized to account for fractional bankruptcy charges. New results including a definition and proof of the ``LTI property'' of the Eisenberg-Noe solvency cascade mechanism lead to explicit $N=\infty$ fixed point equations that arise under very general model specifications. The essential formulas are shown to be implementable via well-defined approximation schemes, but numerical exploration of some of the wide range of potential applications of the method is left for future work.

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  • T. R. Hurd, 2019. "Systemic Cascades On Inhomogeneous Random Financial Networks," Papers 1909.09239, arXiv.org.
  • Handle: RePEc:arx:papers:1909.09239
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    References listed on IDEAS

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    4. T. R. Hurd, 2018. "Bank Panics And Fire Sales, Insolvency And Illiquidity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-30, September.
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