Scenario-free analyses of financial stability with interacting contagion channels
Keywords: indirect exposures
stress tests
liquidity spiral
financial exposures
prudential regulation
interacting contagion channels
multi-layered networks
credit risk
market risk
liquidity risk
macroprudential policy
financial contagion
financial stability
multiplex networks
direct exposures
systemic risk
solvency-liquidity nexus

The Great Financial Crisis of '07/'08 highlighted the dangers of instabilities in financial systems. In unstable financial systems, an initially small and localized financial shock may be amplified and spread throughout the system in a process referred to as financial contagion. Various channels of contagion exist, and propagate shocks through a deterioration of the liquidity and solvency of institutions, decreases in the market prices of tradable securities, etc. Contagion channels interact and amplify one another, such that the channels' collective impact may far exceed the sum of the individual channels' contributions.
Exposures are an important measure of risk that does not rely on an initial stress scenario. When assessing an institution's exposure to the default of a counterparty, traditional exposure measures focus on direct exposures. Since the Global Financial Crisis, indirect exposures via common asset holdings are increasingly recognised too. Yet direct and indirect exposures fail to capture the losses that result from shock propagation and amplification following the counterparty's default. We refer to those spill-over losses as higher-order exposures and contribute to the literature on financial exposures by proposing a way to formalize and quantify them. Using granular data of the South African financial system and a contagion model that captures the most commonly studied contagion channels and their interactions, we show that higher-order exposures make up a significant part of exposures – particularly during times of financial distress when exposures matter most. We also show that higher-order exposures cannot simply be extrapolated from direct or indirect exposures, since they depend strongly on the network structure and the robustness of individual institutions.
As the higher-order exposures we propose capture various contagion channels and their interactions without reliance on an initial stress scenario, they are an objective measure of systemic risks that may go unnoticed when using other measures. Like scenario-based stress tests, however, as a measure of systemic risk higher-order exposures are limited in scope because they only capture the losses that follow from the (idiosyncratic) default of an institution in the system. Yet, financial systems may be subjected to various other kinds of shocks.
Eigenvalue-based approaches study the inherent tendency of a financial system to dampen or amplify shocks, providing a holistic measure of systemic risk. Current eigenvalue-based approaches, however, only handle a single contagion mechanism. We develop an eigenvalue-based approach that gives the best of both worlds, allowing analysis of multiple, interacting contagion channels without the need to impose a subjective stress scenario. This allows us to demonstrate that the instability due to interacting contagion channels can far exceed that of the sum of the individual channels acting alone, which highlights the importance of capturing these interactions. We also derive an analytic formula in the limit of a large number of institutions that elucidates the mechanisms through which interactions between contagion channels amplify instabilities.
We apply the developed eigenvalue-based approach to the data of the South African financial system to study the risk of liquidity spirals emerging that consist of various contagion channels and/or span multiple sectors. We refer to these as complex liquidity spirals and show that the intensity of these liquidity spirals may be severely underestimated when interactions between contagion channels or sectors are overlooked. We capture the collective stability of the banking sector and investment fund sector and show that the stability of the South African financial system strongly depends on how institutions choose to respond to a liquidity shock, with some choices yielding a robust-yet-fragile system. We also show that liquidity spirals are exacerbated when the liquidity of institutions worsens, and that central bank-provided liquidity can greatly dampen liquidity spirals. We study the banking and investment fund sectors' individual contributions to the liquidity spiral and find that market conditions determine which of the two sectors is the main driver of the spiral. The approach developed here can be used to formulate interventions that specifically target the sector that is causing the liquidity spiral.