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 multi-layered financial network that extends the single network of Eisenberg and Noe (2001). 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 also emphasize the value of this general framework in studying a dynamic or multiple maturity setting for financial contagion. We prove that, under standard assumptions  , equilibrium portfolio holdings and market prices exist which clear the multi-layered financial system. However, these clearing solutions are not unique in general . We extend the existence results to consider monotonicity, uniqueness, and sensitivity results under fixed exchange rates between assets. We additionally provide results on the sensitivity of the equilibriumportfolio holdings under misspecification of the system parameters (i. e., initial endowments and interbank liabilities) .  We further provide mathematical formulations for regulatory 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 re-instituted the drachma on a dataset from the European Banking Authority.
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 multi-layered financial network that extends the single network of Eisenberg and Noe (2001). 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 multi-layered financial system. In general, though, these clearing solutions are not unique . We extend this result by considering the t\^atonnement 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 re-instituted the drachma on a dataset from the European Banking Authority.
D
also emphasize the value of this general framework in studying a dynamic or multiple maturity setting for financial contagion. We
A
and without market impacts
R
and market
exist and are unique. However, with market impacts, we prove that equilibrium portfolio holdings and market
R
However,
In general, though,
D
in general
R
the existence results to consider monotonicity, uniqueness, and sensitivity results under fixed exchange rates between assets. We additionally provide results on the sensitivity of the equilibriumportfolio holdings under misspecification of the system parameters (i. e., initial endowments and interbank liabilities)
this result by considering the t\^atonnement process to find the unique attained equilibrium
A
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.
R
regulatory
payment rules