Connectivity and Financial Network Shutdown

Abstract

Connectivity is a measure of the number of connections in a network. It is applied here to financial network shutdown due to inter-institutional default.With the increase in the market for over-the-counter inter- institutional contracts, especially in the interbank market for foreign exchange, interest has increased in the consequences in the consequences of an unwind in payments due to default. This paper is meant to address this interest. To date not one purely descriptive paper has been published on the effects of defaults in payments systems. That paper reports the results of three scenarios for settlement in CHIPS, one of two US dollar payments systems. By contrast, analytic results (not inferred by simulation) on the statistical properties of payments mechanisms are derived here. These results are obtained given the simple clearing mechanisms of no netting and bilateral netting. The model is applied to default propagation in the foreign exchange market. Boolean graphs are used to obtain the results.Since 1797 when Sir Francis Baring introduced the concept of "lender of last resort" concepts such as "too-big-to-fail," "lender-of-last-resort," and systemic risk have belied a need for a quantitative approach to default propagation. Concepts new to finance and economics are introduced. Specifically, those of "network architecture" and "connectivity" of that architecture are defined. Starting from assumptions on the "connection matrix", Markov transition matrices are obtained where each state is the number of firms in default. Debt maturity, connectivity and initial defaults are used to calculate the transition matrices.Besides deriving the stochastic difference equations for the number of failed firms results were obtained on the effect on default propagation of netting liabilities. It is shown that the connectivity value which maximizes the speed of default propagation under netting is not that when liabilities do not offset. For netted liabilities this value is 1/2. For non-offsetting liabilities, this value is 1. The reduction in connectivity by netting, given an initial connectivity g, is shown to be the connectivity squared g^2.Results were obtained demonstrating that when bankruptcy propagation is fast relative to the maturity of obligation the extent of network shutdown can be less than when propagation is slower. Reducing the maturity of obligations definitely increases propagation speed and may increase the extent of default propagation.

JEL Classification: G00