The price of complexity in financial networks.

Financial institutions form multilayer networks by engaging in contracts with each other and by holding exposures to common assets. As a result, the default probability of one institution depends on the default probability of all of the other institutions in the network. Here, we show how small errors on the knowledge of the network of contracts can lead to large errors in the probability of systemic defaults. From the point of view of financial regulators, our findings show that the complexity of financial networks may decrease the ability to mitigate systemic risk, and thus it may increase the social cost of financial crises.

John Snow's legacy: epidemiology without borders.

This Review provides abstracts from a meeting held at the London School of Hygiene and Tropical Medicine, on April 11-12, 2013, to celebrate the legacy of John Snow. They describe conventional and unconventional applications of epidemiological methods to problems ranging from diarrhoeal disease, mental health, cancer, and accident care, to education, poverty, financial networks, crime, and violence. Common themes appear throughout, including recognition of the importance of Snow's example, the philosophical and practical implications of assessment of causality, and an emphasis on the evaluation of preventive, ameliorative, and curative interventions, in a wide variety of medical and societal examples. Almost all self-described epidemiologists nowadays work within the health arena, and this is the focus of most of the societies, journals, and courses that carry the name epidemiology. The range of applications evident in these contributions might encourage some of these institutions to consider broadening their remits. In so doing, they may contribute more directly to, and learn from, non-health-related areas that use the language and methods of epidemiology to address many important problems now facing the world.

Networks and webs in ecosystems and financial systems.

This paper briefly outlines our growing understanding of the relationships between the network structure of ecological networks--both in mathematical models and in the real world--and their consequent dynamical properties. These are interesting, inter alia, because they affect the system's ability to withstand disturbance, whether natural or human-created. The paper also sketches recent interest in the potential relevance of this work to 'systemic risk' and regulatory measures in banking systems, emphasizing the similarities and differences. I conclude with some cautions against drawing excessively general conclusions from any such models.

Size and complexity in model financial systems.

The global financial crisis has precipitated an increasing appreciation of the need for a systemic perspective toward financial stability. For example: What role do large banks play in systemic risk? How should capital adequacy standards recognize this role? How is stability shaped by concentration and diversification in the financial system? We explore these questions using a deliberately simplified, dynamic model of a banking system that combines three different channels for direct transmission of contagion from one bank to another: liquidity hoarding, asset price contagion, and the propagation of defaults via counterparty credit risk. Importantly, we also introduce a mechanism for capturing how swings in "confidence" in the system may contribute to instability. Our results highlight that the importance of relatively large, well-connected banks in system stability scales more than proportionately with their size: the impact of their collapse arises not only from their connectivity, but also from their effect on confidence in the system. Imposing tougher capital requirements on larger banks than smaller ones can thus enhance the resilience of the system. Moreover, these effects are more pronounced in more concentrated systems, and continue to apply, even when allowing for potential diversification benefits that may be realized by larger banks. We discuss some tentative implications for policy, as well as conceptual analogies in ecosystem stability and in the control of infectious diseases.

Individual versus systemic risk and the Regulator's Dilemma.

The global financial crisis of 2007-2009 exposed critical weaknesses in the financial system. Many proposals for financial reform address the need for systemic regulation--that is, regulation focused on the soundness of the whole financial system and not just that of individual institutions. In this paper, we study one particular problem faced by a systemic regulator: the tension between the distribution of assets that individual banks would like to hold and the distribution across banks that best supports system stability if greater weight is given to avoiding multiple bank failures. By diversifying its risks, a bank lowers its own probability of failure. However, if many banks diversify their risks in similar ways, then the probability of multiple failures can increase. As more banks fail simultaneously, the economic disruption tends to increase disproportionately. We show that, in model systems, the expected systemic cost of multiple failures can be largely explained by two global parameters of risk exposure and diversity, which can be assessed in terms of the risk exposures of individual actors. This observation hints at the possibility of regulatory intervention to promote systemic stability by incentivizing a more diverse diversification among banks. Such intervention offers the prospect of an additional lever in the armory of regulators, potentially allowing some combination of improved system stability and reduced need for additional capital.

Systemic risk in banking ecosystems.

In the run-up to the recent financial crisis, an increasingly elaborate set of financial instruments emerged, intended to optimize returns to individual institutions with seemingly minimal risk. Essentially no attention was given to their possible effects on the stability of the system as a whole. Drawing analogies with the dynamics of ecological food webs and with networks within which infectious diseases spread, we explore the interplay between complexity and stability in deliberately simplified models of financial networks. We suggest some policy lessons that can be drawn from such models, with the explicit aim of minimizing systemic risk.

Systemic risk: the dynamics of model banking systems.

The recent banking crises have made it clear that increasingly complex strategies for managing risk in individual banks have not been matched by corresponding attention to overall systemic risks. We explore some simple mathematical caricatures for 'banking ecosystems', with emphasis on the interplay between the characteristics of individual banks (capital reserves in relation to total assets, etc.) and the overall dynamical behaviour of the system. The results are discussed in relation to potential regulations aimed at reducing systemic risk.