To the editors:
In Emanuel Derman’s essay on the Black–Scholes Equation, the French mathematician Louis Jean-Baptiste Alphonse Bachelier is mentioned in passing. Published at the turn of the twentieth century, Bachelier’s PhD thesis was the foundation for the later work of Fischer Black, Myron Scholes, and Robert Merton.1 Scholes and Merton were jointly awarded the 1997 Nobel Prize in Economics for developing “a pioneering formula for the valuation of stock options.”2 Black had passed away in 1995. While brief sketches of Bachelier’s life can be found, no one, as far as I know, has written a full biography. Since Bachelier’s only lasting contribution to mathematics seems to have been his thesis, it is not clear what one would say in such a biography. It is a curious and rather sad story.
Bachelier was born in Le Havre on March 11, 1870.3 His father was a wine merchant. Bachelier would certainly have been headed for one of the grandes écoles, but in 1889 both his parents died. He took over the family wine business and then did his compulsory military service. It was not until 1892 that he was able to begin his studies at the Sorbonne. During this period, he may have worked at the Bourse, although the details remain elusive. In any event, he became interested in the question of how to predict the future price of a stock. It is not clear whether he had heard of Brownian motion, or if he simply invented the idea for himself. He assumed that, on its next move, it was equally likely for the price of a stock to go up or go down. This is Brownian motion. Upon hearing of it for the first time, a natural reaction is to inquire how the price goes anywhere. Of course, after the first move, it is as likely for a price to advance further as it is to go backwards. This results in the random walk that is characteristic of Brownian motion.
Bachelier’s thesis advisor was the great mathematician Henri Poincaré. He found enough merit in Bachelier’s thesis to pass it. This was rather unfashionable mathematics at the time and the work was not greeted with much enthusiasm. Indeed, it is not clear how Bachelier supported himself. From 1910 to 1914, he had an unpaid teaching job at the Sorbonne. He was drafted into the military in 1914 and served until the end of the war. Bachelier then moved around a bit, working temporary academic jobs in Besançon, Dijon, and Rennes. In 1926, he applied for a full professorship at Dijon, but was rejected. A distinguished mathematician, Paul Lévy, had claimed that Bachelier’s work was actually wrong. Lévy later changed his mind when Russian mathematicians, such as Andrey Kolmogorov, began referring to it.4 A year later, Bachelier was finally awarded a professorship at the Université Franche-Comté in Besançon, where he worked until his retirement. He died in Brittany at Saint-Servan-sur-Mer on April 28, 1946. If he had lived a few years longer, Bachelier would have been able to observe the rediscovery of his work by Paul Samuelson and a little later by Black, Scholes, and Merton.5
