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 a shock, which is observed only by the informed investor. We provide conditions under which the informed investor’s asset demands contain information about the shock. These conditions imply that adding derivative securities in some widely studied economies with one risky asset does not reveal any additional information about the shock. We also show that introducing volatility derivatives in incomplete markets makes these markets effectively complete, that is, allows investors to achieve Pareto optimal asset allocations. We find asset prices in closed form in (effectively) complete markets, and show that they preserve the properties of prices in incomplete markets.

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

JEL Classification: D82, G12, G14