Contagion and Equilibria in Diversified Financial Networks
72 Pages Posted: 1 Dec 2021
Date Written: November 30, 2021
Diversified cross-shareholding networks are thought to be more resilient to shocks, but diversification also increases the channels by which a shock can spread. To resolve these competing intuitions we introduce a stochastic model of a diversified cross-shareholding network in which a firm’s valuation depends on its cash endowment and the shares it owns in other firms. We show that a concentration of measure phenomenon emerges: almost all realized network instances drawn from any probability distribution in a wide class are resilient to contagion if endowments are sufficiently large. Furthermore, the size of a shock needed to trigger widespread default increases with the exposure of firms to each other. Distributions in this class are characterized by the property that a firm’s equity shares owned by others are weakly dependent yet lack “dominant” shareholders.
Keywords: financial network, random network, contagion, systemic risk, equilibrium, dynamics, concentration of measure
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