Bank Value and Financial Fragility
We propose a valuation model for a bank which faces a bankruptcy risk. Banks are identified with a possibly infinite random sequence of net benefits. A bank is solvent as long as its benefits remain non-negative. To preserve distressed banks from destruction, banks will be pooled within a financial coalition. When possible, those with current positive balance sheet will refinance those in need of liquidity. Banks are refinanced to the extent that their current needs for liquidity do not exceed their expected endogenous continuation value. This value itself is affected by future refinancing possibilities. We provide a recursive formula to compute this value when there is an aggregate liquidity constraint.
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