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Pricing of Non-redundant Derivatives in a Complete Market

Author

Listed:
  • 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)

  • Koehl Pierre-François

    (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)

  • Abdelhamid Bizid

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider a complete financial market with primitive assets and derivatives on these primitive assets. Nevertheless, the derivative assets are non-redundant in the market, in the sense that the market is complete, only with their existence. In such a framawork, we derive an equilibrium restriction on the admissible prices of derivatives assets. The equilibrium condition imposes a well-ordering principle equivalent martingale measures. This restriction is preference free and applies whenever the utility functions belong to the general class of Von-Neumann Morgenstern functions. We provide numerical examples that show the applicability of restriction for the computation of option prices

Suggested Citation

  • Elyès Jouini & Koehl Pierre-François & Abdelhamid Bizid, 1998. "Pricing of Non-redundant Derivatives in a Complete Market," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00167151, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00167151
    DOI: 10.1007/BF01574150
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00167151
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    References listed on IDEAS

    as
    1. Martin Schweizer, 1995. "Variance-Optimal Hedging in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 1-32, February.
    2. A, Bizid & Elyès Jouini & Pf. Koehl, 1997. "Pricing in Incomplete Markets : An Equilibrium Approach," Working Papers 97-41, Center for Research in Economics and Statistics.
    3. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-732, May.
    4. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 1997. "Pricing and Hedging Derivative Securities in Incomplete Markets: An E-Aritrage Model," NBER Working Papers 6250, National Bureau of Economic Research, Inc.
    5. Detemple, Jerome B & Selden, Larry, 1991. "A General Equilibrium Analysis of Option and Stock Market Interactions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(2), pages 279-303, May.
    6. Bertsimas, Dimitris. & Kogan, Leonid, 1974- & Lo, Andrew W., 1997. "Pricing and hedging derivative securities in incomplete markets : an e-arbitrage approach," Working papers WP 3973-97., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    7. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. repec:bla:jfinan:v:53:y:1998:i:2:p:499-547 is not listed on IDEAS
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    Cited by:

    1. Bizid, Abdelhamid & Jouini, Elyès, 2005. "Equilibrium Pricing in Incomplete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(4), pages 833-848, December.
    2. Marc Rieger, 2011. "Co-monotonicity of optimal investments and the design of structured financial products," Finance and Stochastics, Springer, vol. 15(1), pages 27-55, January.

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    More about this item

    Keywords

    pricing;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets

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