Prudential Regulation in Financial Networks

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  • 1 September 2020
    • preprint
    • Published by HAL in HAL
Abstract
We analyze risk-taking regulation when financial institutions are linked through shareholdings. We model regulation as an upper bound on institutions' default probability, and pin down the corresponding limits on risk-taking as a function of the shareholding network. We show that these limits depend on an original centrality measure that relies on the cross-shareholding network twice: (i) through a risk-sharing effect coming from complementarities in risk-taking and (ii) through a resource effect that creates heterogeneity among institutions. When risk is large, we find that the risk-sharing effect relies on a simple centrality measure: the ratio between Bonacich and self-loop centralities. More generally, we show that an increase in cross-shareholding increases optimal risk-taking through the risk-sharing effect, but that resource effect can be detrimental to some banks. We show how optimal risk-taking levels can be implemented through cash or capital requirements, and analyze complementary interventions through key-player analyses. We finally illustrate our model using real-world financial data and discuss extensions toward including debt-network, correlated investment portfolios and endogenous networks.
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