THREE ESSAYS ON CAPITAL INSURANCE AND TOO BIG TO FAIL BANKS
Analytics
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Abstract
This research study presents an insurance framework of the bank capital by introducinga new type of capital, namely, an insurance capital. A bank pays the insurancecapital to an entity which injects a pre-determined payout of capital during the periodof systemic crisis. The pre-determined payout relies on the aggregate loss of a banksector, so this contract between the bank and the entity is a capital insurance contract.In a rational equilibrium setting, the entity charges an appropriate premiumwhile the banks purchase an optimal amount of the insurance.Chapter I presents a welfare analysis of several capital insurance programs in a rationalexpectation equilibrium setting. We first characterize explicitly the equilibriumof each capital insurance program. Then, we demonstrate that a capital insuranceprogram based on the aggregate loss is better than the classical insurance when thosebig financial institutions have similar expected loss exposures. By contrast, the classicalinsurance is more desirable when the bank's individual risk is consistent with theexpected loss in a precise way. Our analysis shows that the capital insurance programis a useful tool to hedge the systemic risk from the regulatory perspective.As an extension, Chapter II demonstrates that, both the entity and the banks havemotivations to participate in this capital insurance program due to their increasedexpected utilities (welfare) respectively. The total systemic risk ex post within thecapital insurance program is reduced and can be even removed eventually after repeatedly entering the capital insurance program.In Chapter III, we develop a rational expectation equilibrium of capital insurance toidentify too big to fail banks. We show that (1) too big to fail banks can be identifiedby loss betas, a new systemic risk measure through this equilibrium analysis, of allbanks in the entire financial sector by an explicit algorithm; (2) the too big to failfeature can be largely justified by a high level of loss beta; (3) the capital insuranceproposal benefits market participants and reduces the systemic risk; (4) the implicitguarantee subsidy can be estimated within this equilibrium framework; and (5) thecapital insurance proposal can be used to resolve the moral hazard issue. The modelis further tested empirically to identify too big to fail banks during both pre-crisis andpro-crisis periods. Implementing the proposed methodology, we document that thetoo big to fail issue has been considerably reduced in the pro-crisis period. As a result,we demonstrate that the capital insurance proposal could be a useful macro-regulationinnovation policy tool.