Obligations with physical delivery in a multilayered financial network

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Abstract

This paper provides a general framework for modeling financial contagion in a system with obligations in multiple illiquid assets (e.g., currencies). In so doing, we develop a multilayered financial network that extends the single network of Eisenberg and Noe [Management Sci., 47 (2001), pp. 236-249]. In particular, we develop a financial contagion model with fire sales that allows institutions to both buy and sell assets to cover their liabilities in the different assets and act as utility maximizers. We prove that, under standard assumptions and without market impacts, equilibrium portfolio holdings exist and are unique. However, with market impacts, we prove that equilibrium portfolio holdings and market prices exist which clear the multilayered financial system. In general, though, these clearing solutions are not unique. We extend this result by considering the tâtonnement process to find the unique attained equilibrium. The attained equilibrium need not be continuous with respect to the initial shock; these points of discontinuity match those stresses in which a financial crisis becomes a systemic crisis. We further provide mathematical formulations for payment rules and utility functions satisfying the necessary conditions for these existence and uniqueness results. We demonstrate the value of our model through illustrative numerical case studies. In particular, we study a counterfactual scenario on the event that Greece reinstituted the drachma on a dataset from the European Banking Authority.

Original languageEnglish
Pages (from-to)877-906
Number of pages30
JournalSIAM Journal on Financial Mathematics
Volume10
Issue number4
DOIs
StatePublished - 2019

Keywords

  • Financial contagion
  • Financial network
  • Fire sales
  • Systemic risk
  • Tâtonnement process

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