Clearing models for systemic risk assessment in interbank networks

Abstract

In this thesis I consider the problem of clearing models used for systemic risk assessment in interbank networks. I investigate two extensions of the classical Eisenberg & Noe (2001) model. The first extension permits the analysis of networks with interbank liabilities of several maturities. I describe a clearing mechanism that relies on a fixed-point formulation of the vector of each bank’s liquid assets at each maturity date for a given set of defaulted banks. This formulation is consistent with the main stylised principles of insolvency law, permits the construction of simple dynamic models and furthermore demonstrates that systemic risk can be underestimated by single maturity models. In the context of multiple maturities, specifying a set of defaulted banks is challenging. Two approaches to overcome this challenge are proposed. The algorithmic approach leads to a well-defined liquid asset vector for all financial networks with multiple maturities. The simpler functional approach leads to the definition of the liquid asset vector that need not exist but under a regularity condition does exist and coincides with the algorithmic approach. The second extension concerns the non-uniqueness of clearing solutions. When more than one solution exists, the standard approach is to select the greatest solution. I argue that there are circumstances when finding the least solution is desirable. An algorithm for constructing the least solution is proposed. Moreover, the solution is obtainable under an arbitrary lower bound constraint. In models incorporating default costs, clearing functions can be discontinuous, which renders the problem of constructing the least clearing solution non-trivial. I describe the properties of the construction algorithm by means of transfinite sequences and show that it always terminates. Unlike the construction of the greatest solution, the number of steps taken by the algorithm need not be bounded by the size of the network.