Interbank Clearing in Financial Networks with Multiple Maturities

33 Pages Posted: 27 Apr 2018

See all articles by Michael Kusnetsov

Michael Kusnetsov

London School of Economics & Political Science (LSE) - Department of Mathematics

Luitgard Anna Maria Veraart

London School of Economics & Political Science (LSE) - Department of Mathematics

Multiple version iconThere are 3 versions of this paper

Date Written: April 12, 2018

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.

Keywords: systemic risk, default, multiple maturities, clearing, financial networks

JEL Classification: C30, C60, C62, G01, G21, G33, E42, E58

Suggested Citation

Kusnetsov, Michael and Veraart, Luitgard Anna Maria, Interbank Clearing in Financial Networks with Multiple Maturities (April 12, 2018). Available at SSRN: https://ssrn.com/abstract=3161571 or http://dx.doi.org/10.2139/ssrn.3161571

Michael Kusnetsov

London School of Economics & Political Science (LSE) - Department of Mathematics ( email )

Houghton Street
GB-London WC2A 2AE
United Kingdom

Luitgard Anna Maria Veraart (Contact Author)

London School of Economics & Political Science (LSE) - Department of Mathematics ( email )

Houghton Street
GB-London WC2A 2AE
United Kingdom

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