Interbank Clearing in Financial Networks with Multiple Maturities

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). We show that under a regularity condition clearing vectors in a multiple maturity setting can be characterised as fixed points and a greatest and a least clearing vector exists. Clearing vectors in multiple maturity systems are in general not unique, not even under conditions that guarantee uniqueness in a single maturity system.In the absence of the regularity condition, these fixed point do not necessarily exist. We develop the concept of a generalised clearing vector that is well defined for all financial networks with multiple maturities and reduces to the greatest clearing vector under the regularity condition. We show that the generalised clearing vector is consistent with the main stylised principles of insolvency law.Our analysis demonstrates that systemic risk can be underestimated by single maturity models