Interbank Clearing in Financial Networks with Multiple Maturities

Abstract

We consider the problem of systemic risk assessment in interbank networks in which interbank liabilities can have multiple maturities. In particular, we allow for both short-term and long-term interbank liabilities. We develop a clearing mechanism for the interbank liabilities to deal with the default of one or more market participants. Our approach generalises the clearing approach for the single maturity setting proposed by Eisenberg & Noe (2001). Our clearing mechanism focuses on the vector of each bank's liquid assets at each maturity date and develops a fixed-point formulation of this vector for a given set of defaulted banks. Our formulation is consistent with the main stylised principles of insolvency law. We show that in the context of multiple maturities, specifying a set of defaulted banks is challenging. We propose two approaches to overcome this challenge: First, we propose an algorithmic approach for defining the default set and show that this approach leads to a well-defined liquid asset vector for all financial networks with multiple maturities. Second, we propose a simpler functional approach which leads to a functional liquid asset vector which need not exist but under a regularity condition does exist and coincides with the algorithmic liquid asset vector. Our analysis permits construction of simple dynamic models and furthermore demonstrates that systemic risk can be underestimated by single maturity models.

Distress and default contagion in financial networks

“…Throughout this paper, we assume that all contracts have the same maturity date . For an analysis with multiple maturities, we refer to Kusnetsov and Veraart (2019).…”

“…Bankruptcy of an institution has been considered as the only potential trigger of a contagion mechanism in a large part of the literature on solvency contagion: this applies not only to the stream of work building on the clearing approach by Eisenberg and Noe (2001) such as Cifuentes, Ferrucci, and Shin (2005), Rogers and Veraart (2013), Weber and Weske (2017), Kusnetsov and Veraart (2019), and Feinstein (2019) but also to several other default cascade models such as Furfine (2003) Gai and Kapadia (2010), and Amini, Cont, and Minca (2016). We will refer to contagion that is triggered by default as default contagion .…”

Collateralized Networks

“…Obstacles to defining clearing payments arise in other extensions of Eisenberg and Noe [17] as well. Elsinger [18] redefines clearing vectors to cover cross-holdings of debt and equity among banks; David and Lehar [12] consider clearing payments when debt is subject to renegotiation; Kusnetsov and Veraart [32] propose a detailed algorithm to handle debt with different maturities; Jackson and Pernoud [30] note that clearing payments may not be well-defined when banks buy credit protection on other banks, and Banerjee and Feinstein [3] similarly preclude banks from speculating on other banks. None of these extensions fits our setting.…”

Clearing Payments in Dynamic Financial Networks

“…In Capponi & Chen (2015), Ferrara et al (2019) a multi-period clearing framework is introduced. Using a similar approach, Kusnetsov & Maria Veraart (2019) considers the case where interbank liabilities can have multiple maturities, considering both long-term and short-term liabilities.…”