This clearly depends on the specic structure of the

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Unformatted text preview: of i’s liabilities begins to decrease, reflecting the mark-to-market impact of i’s deteriorating credit quality. In the example of Figure 2(a), suppose the central node is at its minimum capital cushion before experiencing a shock; in other words (1 + k )¯i = 150, which implies that k = 1/14. A shock of 5 to the p central node’s outside assets reduces the total value of its liabilities by 5η , so each peripheral node incurs a mark-to-market loss of 5η/14. In contrast, in the original model with η = 0, the peripheral nodes do not experience a loss unless the shock to the central node exceeds 10. As this example illustrates, mark-to-market losses from credit deterioration and bankruptcy costs operate in qualitatively different ways, even though both increase overall losses. Bankruptcy costs amplify the propagation of shortfall. In contrast, accounting for credit quality effectively increases the linkages between nodes. It does so by propagating losses at higher levels of asset values, rather than by amplifying the losses as they are propagated. Shocks can also be propagated through prices due to common exposures or fire sales that go beyond the network of direct obligations, as in Allen and Gale (2000), Cifuentes, Ferrucci, and Shin (2005), and Caccioli et al. (2012). 7 Concluding Remarks In this paper we have argued that it is relatively difficult to generate contagion solely through spillover losses in a network of payment obligations. For contagion to occur, a shock to one node must lead to losses at another set of nodes sufficiently large to wipe out their initial equity (or net worth). This means that either the initial shock must be large (and therefore improbable) relative to the net worth of the infecting node, or that the net worth of the infected nodes must be small. More generally, the probability 27 of contagion depends on the comparative net worths of the various nodes, their level of leverage, and the extent to which the infecting node has obligations to the rest of the financial sector. As Theorems 1 and 2 show, one can compare the probability of contagion and direct default under a wide range of shock distributions without knowing the topological details of the network. The network structure matters more for the amplification effect, in which losses among defaulting nodes multiply because of their obligations to one another. The degree of amplification is captured by the concept of node depth, which is the expected number of periods it takes to exit from the default set from a given starting point. This clearly depends on the specific structure of the interbank obligations, and is dual to the concept of eigenvector centrality in the networks literature. As Theorem 3 shows one can place an upper bound on the amplification effect based on banks’ maximum connectedness with the rest of the financial system (the parameter β + ) without knowing any details of the connections within the system. The network structure...
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This document was uploaded on 02/20/2014 for the course ECON 101 at Pontificia Universidad Católica de Chile.

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