Another Proof of the Existence of GEI Equilibrium with Default and Exogenous Collateral

Abstract

The existence of equilibria in a GEI model with default where short sales are backed by collateral (henceforth: exogenous collateral economy), has been demonstrated by Geanakoplos and Zame in a 2002 version of their paper (“Collateral, Default and Market Crashes”). On the other hand, Araújo et al. (2005) have recently provided a character- ization, via non arbitrage, of prices of defaultable assets backed by collateral. The aim of this paper is to provide an alternative proof of the existence of equilibria in an exoge- nous collateral economy by combining the demand approach used by Geanakoplos and Zame, and the characterization of collateralized asset prices offered by Araújo, Fajardo and Pascoa.