Noisy Arrow-Debreu Equilibria

Abstract

I develop a noisy rational expectations equilibrium model with a continuum of states and a full set of options that render the market complete. I show a major difference in equilibrium behaviour between models with constant absolute risk aversion (CARA) and non-CARA preferences. First, when informed traders have non-CARA preferences, all equilibria are fully revealing, independent of the amount of noise in the supply. Second, when informed traders have CARA preferences, but uninformed traders have non-CARA preferences, the set of equilibria contains a fully revealing equilibrium and a minimally revealing equilibrium. The latter reveals the minimal possible amount of information and is highly inefficient: In this equilibrium, Arrow-Debreu state prices are not sufficient to recover the information contained in the noisy aggregate demand and supply. My results have important implications for price discovery through options.