TY - JOUR
T1 - Obligations with physical delivery in a multilayered financial network
AU - Feinstein, Zachary
N1 - Publisher Copyright:
© 2019 Society for Industrial and Applied Mathematics.
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Financial contagion
KW - Financial network
KW - Fire sales
KW - Systemic risk
KW - Tâtonnement process
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U2 - 10.1137/18M1194729
DO - 10.1137/18M1194729
M3 - Article
AN - SCOPUS:85071988152
VL - 10
SP - 877
EP - 906
JO - SIAM Journal on Financial Mathematics
JF - SIAM Journal on Financial Mathematics
IS - 4
ER -