Endogenous collateral

Abstract

We study an economy where there are two types of assets. Consumers' promises are the primitive defaultable assets secured by collateral chosen by the consumers themselves. These personalized assets are purchased by financial intermediaries who finance these purchases by selling back derivatives to consumers. We show that non-arbitrage prices of primitive assets are strict submartingales, whereas non-arbitrage prices of derivatives are supermartingales. Next we establish existence of equilibrium, without imposing bounds on short-sales. The nonconvexity of the budget set is overcome by considering a continuum of agents.

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

“…Araújo et al (2005) have characterized, via non-arbitrage, the collateralized asset prices. Although their result was obtained in the endogenous collateral setting, the authors provided a similar result for the exogenous case (see Corollary 1 below) which will be fundamental for our purpose.…”

“…On the other hand, the prices of collateralized assets have recently been characterized via arbitrage by Araújo et al (2005) for the case in which uncertainty is represented by a finite number of states of nature. For the case of a continuum of states this characterization has recently been extended by Orrillo (2002).…”

“…For the case of a continuum of states this characterization has recently been extended by Orrillo (2002). In contrast to the methodology used by Geanakoplos and Zame (2002), Araújo et al (2005) used their asset price characterization to establish their existence result without using the demand approach. Instead, they used the generalized game approach of Debreu (1952).…”

“…To reach our goal, we combine the characterization of asset prices offered by Araújo et al (2005) and the demand approach used by Geanakoplos and Zame (2002). The proof follows lines similar to the usual proof of existence in an exchange economy with complete market structure (see Hildenbrand (1974), or the proof followed by Werner (1985) or Zhang (1996) in the case of incomplete financial markets).…”

“…On the other hand, Araújo et al (2005) have recently provided a characterization, 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 exogenous 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.…”