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A discrete stochastic model for investment withan application to the transaction costs case

Author

Listed:
  • Laurence Carassus

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

  • Elyès Jouini

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique)

Abstract

This work consists of two parts. In the first one, we study a model where the assets are investment opportunities, which are completely described by their cash-flows. Those cash-flows follow some binomial processes and have the following property called stationarity: it is possible to initiate them at any time and in any state of the world at the same condition. In such a model, we prove that the absence of arbitrage condition implies the existence of a discount rate and a particular probability measure such that the expected value of the net present value of each investment is non-positive if there are short-sales constraints and equal to zero otherwise. This extends the works of Cantor–Lippman who studied a deterministic setup. In the second part, we apply this result to a financial model in the spirit of Cox–Ross–Rubinstein Cox, but where there are transaction costs on the assets. This model appears to be stationary. At the equilibrium, the Cox–Ross–Rubinstein's price of a European option is always included between its buying and its selling price. Moreover, if there is transaction cost only on the underlying asset, the option price will be equal to the Cox–Ross–Rubinstein's price. Those results give more information than the results of Jouini–Kallal Jouini, which where working in a finite horizon model.

Suggested Citation

  • Laurence Carassus & Elyès Jouini, 2000. "A discrete stochastic model for investment withan application to the transaction costs case," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00167143, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00167143
    DOI: 10.1016/S0304-4068(99)00005-1
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    Keywords

    stochastic model; transaction costs case;

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