[...]... in-degree (the number of links that point into the node) and an out-degree (the number of links pointing out of the node) Incoming links to a bank reflect the interbank assets of that bank, i.e monies owed to the bank by a counterparty By contrast, the outgoing links correspond to the bank’s interbank liabilities Critically, the joint distribution of the in- and out-degrees governs the potential for the. .. functions 14 The Robust-Yet-Fragile Nature of Financial Systems the distribution of the number of links leaving a vulnerable bank chosen at random; (b) the distribution of links leaving a vulnerable neighbour reached by following a randomly chosen link; (c) the distribution of the cluster sizes of vulnerable banks reached by following a random link; and (d) the distribution of the size of the vulnerable... adjacent to it The likelihood of contagion is, therefore, directly linked to the size of the vulnerable cluster within the window Intuitively, near both the lower and upper phase transitions, the probability of contagion must be close to zero since the size of the vulnerable cluster is either restricted by limited connectivity or by the presence of a high fraction of safe banks The probability of contagion... region, the size of the giant vulnerable cluster corresponds closely to the size of the connected component of the network, meaning that the fraction of the network affected by episodes of contagion is roughly similar to the probability that contagion breaks out But these quantities diverge as z increases, and near the upper phase transition, the system exhibits a robust-yet-fragile tendency—episodes of. .. system-wide stress-testing must address the non-linear consequences implied by the two-way relationship between the financial system and the real economy, together with the sizeable externalities implied by the interconnectedness of financial firms for the system as a whole The chapters that follow tackle these issues They are grouped into three substantive themes: first, financial contagion and the collapse... versions of the model (Aikman et al., 2009; Gauthier et al., 2010) developed at the Bank of England and the Bank of Canada allow for richer balance sheets and funding liquidity risk The attraction for policymakers stems from the story-telling capability of RAMSI While other approaches to systemic risk modelling offer either rigour in terms of microfoundations or consistency with market-based pricing of risk,... interdependencies Together with the growing interconnectedness of the financial system, the size, concentration, and riskiness of banks have increased markedly Financial engineering has facilitated balance sheet growth that is no longer limited by the scale of opportunities in the real economy As King (2010) observes, the size of the US banking sector is currently some 100 per cent of GDP, with the Bank of America... for the one vertex at the end of the initial edge and we have used the fact that if a generating function generates the probability distribution of some property of an object, then the sum of that property over m independent such objects is distributed according to the mth power of the generating function Using equation (2.8) and noting that G1(1) represents the probability that a random neighbour of. .. In the former instance, there are two phase transitions and a continuous window of (intermediate) values of z for which contagion is possible For values of z 18 The Robust-Yet-Fragile Nature of Financial Systems that lie outside the window and below the lower phase transition, the P j;k j Á k Á pjk term is too small and the network is insufficiently connected for contagion to spread; for values of z... From The Financial Times # The Financial Times Limited 2012 All rights reserved Systemic Risk features of the standard economic paradigm, particularly in macroeconomics Trichet emphasizes building models based on bottom-up simulations of individual behaviour rather than top-down maximization in order to generate the non-linearities characteristic of systemic instability, arguing that ‘ seen from the . financial sector—particularly the extent to which financial firms take into account the effects of their actions on the balance sheets of other players. But financial innovation, in the form of credit risk transfer and off-balance. beyond breaking point. The ideas developed by Prasanna Gai and his collaborators trace their origins to this early work by the team at the Bank of England. They show the richness of the conceptual frameworks. description of the quantitative risk assessment framework developed at the Bank of England the Risk Assess- ment Model for Systemic Institutions (RAMSI)—that incorporated the insights of the early