He is credited with being the first person to model the stochastic process now called Brownian motion, as part of his doctoral thesis The Theory of Speculation (Théorie de la spéculation, defended in 1900).

Both of Louis's parents died just after he completed his high school diploma ("baccalauréat" in French), forcing him to take care of his sister and three-year-old brother and to assume the family business, which effectively put his graduate studies on hold.

Defended on 29 March 1900 at the University of Paris,[2] Bachelier's thesis was not well received because it attempted to apply mathematics to an area mathematicians found unfamiliar.

Jean-Michel Courtault et al. point out in "On the Centenary of Théorie de la spéculation"[4] that honorable was "the highest note which could be awarded for a thesis that was essentially outside mathematics and that had a number of arguments far from being rigorous".

For several years following the successful defense of his thesis, Bachelier further developed the theory of diffusion processes, and was published in prestigious journals.

With the support of the Council of the University of Paris, Bachelier was given a permanent professorship at the Sorbonne, but World War I intervened and he was drafted into the French army as a private.