Slide 1

Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance
translated and with a commentary by: Mark Davis and Alison Etheridge
with a foreword by: Paul A Samuelson
Princeton University Press, 2006, 188 pages, £15.14 at

reviewed by:
Professor Michael Mainelli, Executive Chairman, The Z/Yen Group

[An edited version of this article first appeared as “Louis Bachelier’s Theory of Speculation” (Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance translated and with commentary by Mark Davis and Alison Etheridge, foreword by Paul A Samuelson), London Mathematical Society Newsletter, Number 359, London Mathematical Society (May 2007) pages 21-22.]

Louis Jean-Baptiste Alphonse Bachelier (1870-1946) was a French mathematician credited with being the first person to model and apply Brownian motion in his PhD thesis, the “Theory of Speculation” published in 1900.  Bachelier’s work on random walks predates Einstein’s celebrated study of Brownian motion by five years; intriguingly though, Bachelier used his work to explore finance rather than physics.  “Theory of Speculation” is one of the earliest papers to use advanced mathematics in the study of the stochastic processes of finance and the first to introduce the mathematics of option pricing, 73 years before Black-Scholes.  Benoit Mandelbrot believes that the modern theory of finance relies on five men: Louis Bachelier, Harry Markowitz, William Sharpe, and Fisher Black and Myron Scholes.  According to Mandelbrot, the foundations of the Capital Asset Pricing Model, Modern Portfolio Theory and Black-Scholes “all sit on the theoretical foundation laid by Bachelier a century ago”.

Bachelier was born in Le Havre to a wine merchant.  Following his parents’ deaths, Bachelier had to suspend his graduate studies to run the family business, acquiring practical experience of financial markets.  His grades at the Sorbonne were not exceptional, but his instructor, the legendary Henri Poincaré, admired Bachelier’s approach to Gauss’s law of errors in his thesis - “very original and all the more interesting as his reasoning could extend with some changes to the theory of errors itself”. The thesis received a “mention honorable”, rather than “très honorable”, but was accepted for publication in the prestigious Annales Scientifiques de l’École Normale Supérieure.

Bachelier’s subsequent academic career was problematic, starting fitfully at the Sorbonne and then interrupted by World War I.  Bachelier went on to hold temporary positions until he was finally awarded a permanent professorship in 1927 at Besançon, where he worked for 10 years.  Bachelier’s influence on finance and economics may have been smaller than the scale of his insights deserved, but his work in probability was well-regarded, even popular.  Bachelier’s 1914 book, Le Jeu, la Chance et le Hasard (Games, Chance and Risk), reportedly sold over six thousand copies.

Professors Davis and Etheridge have brought out a remarkably friendly book in four chapters – “Mathematics and Finance”, “Théorie de la Spéculation”, “From Bachelier to Kreps, Harrison and Pliska” and “Facsimile of Bachelier’s Original Thesis”. It is a fun, even swift read, belying its length.  With his earned authority, Samuelson extols the importance of Bachelier in the foreword.  Davis and Etheridge set the context in a very human way.  The reader gets to engage with Bachelier directly, and finds his work crosses the gap of a century with ease.  The Sorbonne instructors’ report on the thesis is also included, permitting us to see how it was evaluated in its own time.  The inclusion of Bachelier’s original thesis as a facsimile is a delightful touch, allowing the reader to feel the début de siècle through the typesetting and to delve into portions of the thesis for direct contact, without being intimidated by rusty or poor French.  Davis’ and Etheridge’s discussion of the work’s influence and context in the modern world is incisive without being voluminous.  A few pages of references help to set the thesis in a wider context.  The only material complaint is that there is no index.

This book suits anyone working in quantitative finance.  Bachelier’s thesis engages us formally with the paradox that besets the heart of financial theory, “if markets are random then how do people make money?” In order to find the ‘non-random’ in markets, we must first understand the stochastic theory of markets.  This “illuminating homage to a long underrated science hero” (Samuelson’s words) is a fitting place to start.

Professor Michael Mainelli, PhD FCCA FSI, originally undertook aerospace and computing research, followed by seven years as a partner in a large international accountancy practice before a spell as Corporate Development Director of Europe’s largest R&D organisation, the UK’s Defence Evaluation and Research Agency, and becoming a director of Z/Yen ( Michael is Mercers’ School Memorial Professor of Commerce at Gresham College (

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