Computing Systemic Risk Measures with Graph Neural Networks

TL;DR

This paper extends systemic risk measures to graph-structured financial networks using permutation equivariant neural networks, demonstrating their effectiveness in approximating optimal allocations and minimal bailout capital.

Contribution

It introduces the use of graph neural networks and extended permutation equivariant neural networks for systemic risk measurement in financial networks, showing their superior performance.

Findings

Permutation equivariant neural networks outperform benchmarks in risk approximation.

GNNs effectively model bilateral liabilities in financial networks.

Optimal random allocations can be approximated using proposed neural network architectures.

Abstract

This paper investigates systemic risk measures for stochastic financial networks of explicitly modelled bilateral liabilities. We extend the notion of systemic risk measures from Biagini, Fouque, Fritelli and Meyer-Brandis (2019) to graph structured data. In particular, we focus on an aggregation function that is derived from a market clearing algorithm proposed by Eisenberg and Noe (2001). In this setting, we show the existence of an optimal random allocation that distributes the overall minimal bailout capital and secures the network. We study numerical methods for the approximation of systemic risk and optimal random allocations. We propose to use permutation equivariant architectures of neural networks like graph neural networks (GNNs) and a class that we name (extended) permutation equivariant neural networks ((X)PENNs). We compare their performance to several benchmark allocations. The main feature of GNNs and (X)PENNs is that they are permutation equivariant with respect to the underlying graph data. In numerical experiments we find evidence that these permutation equivariant methods are superior to other approaches.