Multi-Asset Noisy Rational Expectations Equilibrium with Contingent Claims

Abstract

We study a noisy rational expectations equilibrium in a multi-asset economy populated by informed and uninformed investors and noise traders. The assets can include state contingent claims such as Arrow-Debreu securities, assets with only positive payoffs, options or other derivative securities. The probabilities of states depend on an aggregate shock, which is observed only by the informed investor. We derive a three-factor CAPM with asymmetric information, establish conditions under which asset prices reveal information about the shock, and show that information asymmetry amplifies the effects of payoff skewness on asset returns. We also find that volatility derivatives make incomplete markets effectively complete, and their prices quantify market illiquidity and shadow value of information to uninformed investors.

Keywords: asymmetric information, rational expectations, learning from prices, contingent claims, derivative securities

JEL Classification: D82, G12, G14