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Incomplete Markets and Short-Sales Constraints: An Equilibrium Approach

Author

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  • Elyès Jouini

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Abdelhamid Bizid

Abstract

We consider a general discrete-time dynamic financial market with three assets: a riskless bond, a security and a derivative. The market is incomplete (a priori) and at equilibrium. We assume also that the agents of the economy have short-sales constraints on the stock and that the payoff at the expiry of the derivative asset is a monotone function of the underlying security price. The derivative price process is not identified ex ante. This leads the agents to act as if there were no market for this asset at the intermediary dates. Using some nice properties of the pricing probabilities, which are admissible at the equilibrium, we prove that it suffices to consider the subset of the risk-neutral probabilities that overestimate the low values of the security and underestimate its high values with respect to the true probability. This approach greatly reduces the interval of admissible prices for the derivative asset with respect to no-arbitrage, as showed numerically.

Suggested Citation

  • Elyès Jouini & Abdelhamid Bizid, 2001. "Incomplete Markets and Short-Sales Constraints: An Equilibrium Approach," Post-Print halshs-00167147, HAL.
    • Handle: RePEc:hal:journl:halshs-00167147
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    Cited by:

    1. Traian A. Pirvu & Huayue Zhang, 2012. "A Multi Period Equilibrium Pricing Model," Papers 1205.6193, arXiv.org.
    2. Alet Roux, 2007. "The fundamental theorem of asset pricing under proportional transaction costs," Papers 0710.2758, arXiv.org.

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