Financial Assets Promising A Risk Free Payoff

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Banks hold financial assets promising a risk-free payoff equal to $ iskfreeassets$, with households as their counterpart for this financial position. Banks also hold $Facevalue$ government bonds. Each government bond has a face value equal to one, payable at the end of the second period. The government, however, may default on its debt, so the payoff may be lower than one. Let $govtpayoff(Y) leq 1$ be the actual payoff of one government bond, where $Y$ is the aggregate output---the payoff, $govtpayoff(Y)$, will be determined below. One key feature of the mechanism that we describe is that banks ' loans are distorted by the overhang of the existing bank liabilities. To model this feature, we assume that, initially, each bank has financial…show more content…
Let $sigma$ be the standard deviation of $ln(idiosyncraticshock)$. Each bank receives net-of-taxes output, $(1- axrate)y$, in return of its loans.footnote{ To focus on the main mechanism, we lump the financial and production sectors together. The mechanism, however, does not depend on this assumption and would be at work even if firms were modeled separately, banks received only a share of the output produced, and firms distributed the rest to households as dividends.} It also receives the payoff, $assetpayoff(Y)$, of its financial assets and government bonds. If the sum of the two is less than the face value of its liabilities, i.e., $(1- axrate)y+assetpayoff(Y) < facevalue$, then the bank defaults, repays $(1- axrate)y+assetpayoff(Y)$ to the creditors, and does not distribute any dividend. Otherwise, the bank repays the entire face value of its liabilities, $facevalue$, to the creditors and distributes the rest, $(1- axrate)y+assetpayoff(Y)-facevalue$, as dividends. We restrict attention to equilibria where $facevalue > assetpayoff(Y)$, so that there is a positive probability that banks default. Notice that all decisions are made before the realization of the idiosyncratic shock,
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