Multi-asset Noisy Rational Expectations Equilibrium with Contingent Claims

We consider a noisy rational expectations equilibrium in a multi-asset economy populated by informed and uninformed investors, and noise traders. We relax the usual assumption of normally distributed asset payoffs and allow for assets with very general payoff distributions, including non-redundant contingent claims, such as options and other derivatives. We provide necessary and sufficient conditions under which contingent claims provide information about the source of uncertainty in the economy and, hence, reduce the asymmetry of information. We show that introducing a volatility derivative makes incomplete-market economies effectively complete. We also apply our results to pricing risky debt and equity and demonstrate that firms cannot manipulate the information contained in debt and equity prices by changing the face value of debt. Our paper provides a new tractable framework for studying asset prices under asymmetric information. When the market is complete, we derive the equilibrium in closed form. When the market is incomplete, we derive it in terms of easily computable inverse functions.