Obligations with Physical Delivery in a Multilayered Financial Network

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 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 re-instituted the drachma on a dataset from the European Banking Authority.

Capital regulation under price impacts and dynamic financial contagion

“…14,Π i (τ k ) ≥ 0 for all banks i. Let Λ be as in the proof of Lemma 3.14, definethe domain U k = m l=1 Π ∈ [0, 1] n |Λ k l (s ⊤ Π) ≥ 1 2 Λ l (τ k ) whereΛ k : [0, M ] → R m is defined by = ½ {t<τ n−1 }Γ t (t ∧τ k+1 ) f t (t ∧τ k ) 1−αθ min αθ minΛk + ½ {t≥τ n−1 } s i n j=n−1…”

S-shaped transition trajectory and dynamic development frontier of the financial systemic risk research: a multiple networks analysis

“…After applying the method to the European bank's dataset, they found that the perturbation of relative liabilities may lead to huge economic differences, which may underestimate the risk of infection. Banerjee andFeinstein (2019), Feinstein (2019), Veraart (2020), and Barucca et al (2020) explored financial systemic risk from the aspect of interdependent liabilities, a multilayered financial network, stress testing, and credit risk, respectively.…”

Interbank Clearing in Financial Networks with Multiple Maturities

“…Related work is the approach by Feinstein (2017) who considers an extension of the single network approach by Eisenberg & Noe (2001) to a multi-layered financial network to study contagion in multiple asset classes. This approach could also be applied to a multi-period or multi-maturity setting.…”