Adjustable network reconstruction with applications to CDS exposures

Abstract

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.

Distress and default contagion in financial networks

“…If the interbank liabilities are not fully observable, then one can reconstruct this matrix from its observable row and column sums. Several methods are available to do this, see, for example, the Bayesian approach by Gandy and Veraart (2017, 2019) and discussions on alternative approaches. These approaches do not rely on historical estimates of the financial network but reconstruct the financial network based on the partial information that is available on the current network.…”

“…To reevaluate the network, we need to know the individual entries , where , of the liabilities matrix. As these are not available, we use the Bayesian approach to network reconstruction developed by Gandy and Veraart (2017, 2019) to reconstruct a matrix from its row and column sums. In particular, we use the empirical fitness model introduced in Gandy and Veraart (2019) and calibrate it to a network density of 0.4 as described in Gandy and Veraart (2019), that is, 40% of the entries of the matrix are assumed to be nonzero.…”

“…As these are not available, we use the Bayesian approach to network reconstruction developed by Gandy and Veraart (2017, 2019) to reconstruct a matrix from its row and column sums. In particular, we use the empirical fitness model introduced in Gandy and Veraart (2019) and calibrate it to a network density of 0.4 as described in Gandy and Veraart (2019), that is, 40% of the entries of the matrix are assumed to be nonzero. We obtain a sample of liabilities matrices , which have the observed row and column sums.…”

A block-structured model for banking networks across multiple countries

“…A similar approach is presented by Gandy and Veraart [25,26], who consider the same fitness model for the generation of the adjacency matrix as Cimini et al [16], but suggest a Gibbs sampler for weight allocation. The MCMC sampler creates a sequence of weighted networks that all match the row and column sums exactly, and that converges to an exponential distribution w.r.t.…”

“…unweighted directed graphs. In the spirit of Cimini et al [16] and Gandy and Veraart [26], our fitness model accounts for the nodes' heterogeneity and can be calibrated to a desired density. In addition, we incorporate degree reciprocity, i.e.…”