Equilibria with options: Existence and indeterminacy

This paper studies an economy in which trading takes place in spot commodity markets and incomplete futures markets for assets of various types. There are real assets (stocks or commodity futures), options on real assets, and a riskless nominal bond. We show that for a generic set of economies parametrized by consumers' endowments and structure of real assets, there exists an equilibrium. Moreover, we show that, generically, the set of equilibrium allocations of commodities contains a manifold of a high dimension. Even if the market structure is potentially complete (i.e., the number of assets, including options, equals or exceeds the number of states of nature) and the Arrow-Debreu equilibrium can be achieved through sequential trading in spot and futures markets, there are multiple (inefficient) equilibria without full rank of the asset payoff matrix.