INCOMPLETE MARKETS AND SHORT-SALES CONSTRAINTS: AN EQUILIBRIUM APPROACH

A. Bizid () and Elyès Jouini ()
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A. Bizid: CERMSEM-Université Paris I and CDC IXIS-Capital Markets, 56, rue de Lille, 75007 Paris, France

International Journal of Theoretical and Applied Finance (IJTAF), 2001, vol. 04, issue 02, 211-243

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 identifiedex 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.

Keywords: Incomplete markets; information modelling; equilibrium; option pricing; short-sales constraints; trees (search for similar items in EconPapers)
Date: 2001
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Working Paper: Incomplete Markets and Short-Sales Constraints: An Equilibrium Approach (2001)
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DOI: 10.1142/S0219024901000936

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