# Obligations with Physical Delivery in a Multi-Layered Financial Network

## TL;DR

This paper extends the financial network model to multiple illiquid assets, analyzing contagion, market impacts, and equilibrium conditions, with applications to systemic risk and a case study on Greece re-instituting the drachma.

## Contribution

It develops a multi-layered financial network model with market impacts, proving existence and uniqueness of equilibria and analyzing systemic crisis points.

## Key findings

- Equilibrium portfolios exist and are unique without market impacts.
- Market impacts lead to existence of equilibrium but not necessarily uniqueness.
- Discontinuities in equilibrium relate to systemic crises.

## 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 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.