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This paper is concerned with systemic risk in an interbank market, modelled as a directed graph of interbank obligations. This builds on the modelling paradigm of Eisenberg and Noe [Eisenberg L, Noe TH (2001) Systemic risk in financial systems. Management Sci. 47(2):236–249] by introducing costs of default if loans have to be called in by a failing bank. This immediately introduces novel and realistic effects. We find that, in general, many different clearing vectors can arise, among which there is a greatest clearing vector, arrived at by letting banks fail in succession until only solvent banks remain. Such a collapse should be prevented if at all possible. We then study situations in which consortia of banks may have the means and incentives to rescue failing banks. This again departs from the conclusions of the earlier work of Eisenberg and Noe, where in the absence of default losses there would be no incentive for solvent banks to rescue failing banks. We conclude with some remarks about how a rescue consortium might be constructed. This paper was accepted by Wei Xiong, finance.

We develop a Bayesian methodology for systemic risk assessment in financial networks such as the interbank market. Nodes represent participants in the network and weighted directed edges represent liabilities. Often, for every participant, only the total liabilities and total assets within this network are observable. However, systemic risk assessment needs the individual liabilities. We propose a model for the individual liabilities, which, following a Bayesian approach, we then condition on the observed total liabilities and assets and, potentially, on certain observed individual liabilities. We construct a Gibbs sampler to generate samples from this conditional distribution. These samples can be used in stress testing, giving probabilities for the outcomes of interest. As one application we derive default probabilities of individual banks and discuss their sensitivity with respect to prior information included to model the network. An R-package implementing the methodology is provided.

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.

This paper is concerned with reconstructing weighted directed networks from the total in-and out-weight of each node. This problem arises for example in the analysis of systemic risk of partially observed financial networks. Typically a wide range of networks is consistent with this partial information. We develop an empirical Bayesian methodology that can be adjusted such that the resulting networks are consistent with the observations and satisfy certain desired global topological properties such as a given mean density, extending the approach by Gandy and Veraart (2017). Furthermore we propose a new fitness-based model within this framework. We provide a case study based on a data set consisting of 89 fully observed financial networks of credit default swap exposures. We reconstruct those networks based on only partial information using the newly proposed as well as existing methods. To assess the quality of the reconstruction, we use a wide range of criteria, including measures on how well the degree distribution can be captured and higher order measures of systemic risk. We find that the empirical Bayesian approach performs best.