Equilibria with options: Existence and indeterminacy

Stefan Krasa, Jan Werner

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)305-320
Number of pages16
JournalJournal of Economic Theory
Issue number2
StatePublished - Aug 1991

ASJC Scopus subject areas

  • Economics and Econometrics


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