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Louis Bachelier's Théorie de la spéculation : The missing piece in Walras' general equilibrium

Author

Listed:
  • Nicole El Karoui

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique - UPCité - Université Paris Cité)

  • Antoine Parent

    (LED - Laboratoire d'Economie Dionysien - UP8 - Université Paris 8 Vincennes-Saint-Denis, OFCE - Observatoire français des conjonctures économiques (Sciences Po) - Sciences Po - Sciences Po, CAC-IXXI, Complex Systems Institute)

  • Pierre-Charles Pradier

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We propose a revisited view of Louis Bachelier's contribution to economic analysis. Conventional wisdom presents Bachelier as the founding father of modern financial theory. We show that Bachelier's work is constructed to respond to a gap in the Walrasian general equilibrium, where the options market is verbosely introduced but not modeled. By providing a price formation theory for the missing options market, Bachelier undoubtedly presents himself as the heir apparent of the mathematical economics tradition founded by Walras. Indeed, Bachelier's methodological stance is clearly formed on the "rational method" of Walras, proceeding by mathematical demonstration from postulates that we make explicit. We show additionally how Walras and Bachelier in pre-WW2 France reached to the same audience. We propose to name this augmented general equilibrium model the Walras-Bachelier model of intertemporal general equilibrium in the presence of risk. This theory prefigures the Arrow-Debreu model, with some differences which we make clear.

Suggested Citation

  • Nicole El Karoui & Antoine Parent & Pierre-Charles Pradier, 2022. "Louis Bachelier's Théorie de la spéculation : The missing piece in Walras' general equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03815600, HAL.
    • Handle: RePEc:hal:cesptp:halshs-03815600
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03815600v1
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    References listed on IDEAS

    as
    1. Walter Schachermayer & Josef Teichmann, 2008. "How Close Are The Option Pricing Formulas Of Bachelier And Black–Merton–Scholes?," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 155-170, January.
    2. Franck Jovanovic, 2012. "Bachelier: Not the forgotten forerunner he has been depicted as. An analysis of the dissemination of Louis Bachelier's work in economics," The European Journal of the History of Economic Thought, Taylor & Francis Journals, vol. 19(3), pages 431-451, September.
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    More about this item

    Keywords

    General equilibrium; Financial markets; Option pricing; Bachelier; Walras;
    All these keywords.

    JEL classification:

    • B13 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Neoclassical through 1925 (Austrian, Marshallian, Walrasian, Wicksellian)
    • B16 - Schools of Economic Thought and Methodology - - History of Economic Thought through 1925 - - - Quantitative and Mathematical
    • B31 - Schools of Economic Thought and Methodology - - History of Economic Thought: Individuals - - - Individuals
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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