Recourse in a collateral equilibrium model

Abstract

Recourse is introduced to the binomial collateral equilibrium model described by Geanakoplos and Fostl in their Econometrica paper "Leverage and default in binomial economies: A complete characterization". First, the paper's main results, culminating in the binomial no-default theorem, are examined in this generalized setting. This theorem ensures that any collateral equilibrium can be translated to a default-free equilibrium with the same prices and identical allocations of goods, yet different debt contract and asset allocations. It is shown that the theorem is valid in specific circumstances only. Then, welfare considerations are introduced. Examples motivate the conjecture that in an equilibrium in which the collateral is scarce and borrowing is maximal, every investor's utility can be improved upon by increasing the recovery rate. Even though, closed-form expressions for marginal utility changes are derived, attempts to prove that they are positive were not successful yet.