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.Although global financial systems have seen considerable growth in size, concentration, and complexity over the past few decades (1), our understanding of the dynamic behavior of such systems has not necessarily kept pace. Indeed, the current financial crisis has presented a stark demonstration of the potential for modern financial systems to amplify and disseminate financial distress on a global scale. From a regulatory perspective, these events have prompted fresh interest in understanding financial stability from a system level. In particular, although precrisis regulation (as typified by the Basel II accords) sought to minimize the risk of failure of individual banks irrespective of systemic importance, new regulation will seek to target the systemic consequences of bank collapse as well. To quote Haldane and May (2), “What matters is not a bank’s closeness to the edge of the cliff; it is the extent of the fall.”In this context, a clear feature of interest is the presence of large, highly connected banks. These banks have conceptual parallels in biology: simple models have been influential in underlining the importance of “superspreaders” in the spread and control of infectious diseases (3, 4), and “keystone” species are thought to serve a valuable role in ecosystem stability (5, 6). Here we develop dynamic models to apply and extend these lessons to financial systems. Our approach is theoretical, and our models necessarily oversimplified. Nonetheless, by considering transmission mechanisms specific to modern financial systems, our approach recognizes some important differences between these and other complex systems. We show how, even with such distinctions, the basic insights deriving from our model allow us to draw certain parallels with other situations where size and complexity are important.If financial crises may be compared with forest fires, causes for the initiating sparks pose important questions in their own right: for example, the role of excessive leverage and credit growth (7) or the pricing for complex financial instruments (8, 9). Here, however, our focus is on the role of large banks in the “flammability” of the system, or its capacity for amplification and propagation of an initiating shock. We ask the following questions: How does the impact of a bank’s collapse scale with its size? How might capital adequacy standards seek to mitigate this impact? More broadly, what is the effect of concentration and diversification on system stability?Network approaches (10–14) are well-suited for such questions, particularly in modeling contagion that is transmitted through linkages in the financial system. Here we adopt such an approach to bring together three important transmission channels into a unified framework: (i) liquidity hoarding, where banks cut lending to each other as a defensive measure (1, 15); (ii) asset price contagion linked to market illiquidity (16–18); and (iii) the propagation of defaults via counterparty credit risk (19–21).Although the network effects listed above act on defined webs of connectivity, confidence effects can operate more broadly, with the overall state of the system potentially influencing an individual bank’s actions, and vice versa. This motivates a special feature of our model, which explicitly integrates network dynamics with confidence effects.The interaction of such network and confidence effects arguably played a major role in the collapse of the interbank market (a network of lending exposures among banks) and global liquidity “freeze” that occurred during the crisis (22). Interbank loans have a range of maturities, from overnight to a matter of years, and may often be renewed, or rolled over, at the point of maturity. A pronounced feature of the 2007/2008 crisis was that, as the system deteriorated, banks stopped lending to each other at all but the shortest maturities (7, 29). The bankruptcy of Lehman Brothers in September 2008 transmitted distress further across the financial network, and signaled that there was no guarantee of government support for institutions in distress. The effects extended well beyond those institutions directly exposed to Lehman Brothers, with banks throughout the system withdrawing interbank lending outright and propagating distress to the real economy by sharply contracting household and corporate lending (23). At the time of writing, ongoing events illustrate the potential for similar dynamics in the context of sovereign and banking sector distress in some Eurozone countries.Several specific motivating factors have been proposed to explain “liquidity hoarding” (the maturity-shortening and ultimate withdrawal of interbank lending): precautionary measures by lending banks in anticipation of future liquidity shortfalls, counterparty concerns over specific borrowing banks, or collapses in overall system confidence (24, 25). Our framework parsimoniously incorporates all of these mechanisms, but also captures the idea that a bank’s distress may affect not just those directly exposed or linked to it, but also confidence in the market at large.In what follows we summarize essential features of the model structure, with details provided in Materials and Methods, and a summary of model parameters and their default values given in Table S1. We use this model to explore the impact of an initiating shock, with particular reference to the nonlinearities arising from each of the contagion channels modeled, the effects of size disparity among banks and system concentration, and the effects of diversification. We then outline tentative implications for regulatory capital requirements before discussing important caveats to our work. Throughout the paper, we abstract from extraordinary policy intervention in crisis, so that liquidity cannot be obtained more easily from the central bank than from the market, and failing institutions are not bailed out.