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

Résumé En

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.