Louis Bachelier's Theory of Speculation: The Origins of Modern Finance

Louis Bachelier's Theory of Speculation: The Origins of Modern Finance

Louis Bachelier's Theory of Speculation: The Origins of Modern Finance

Louis Bachelier's Theory of Speculation: The Origins of Modern Finance


March 29, 1900, is considered by many to be the day mathematical finance was born. On that day a French doctoral student, Louis Bachelier, successfully defended his thesis Théorie de la Spéculation at the Sorbonne. The jury, while noting that the topic was "far away from those usually considered by our candidates," appreciated its high degree of originality. This book provides a new translation, with commentary and background, of Bachelier's seminal work.

Bachelier's thesis is a remarkable document on two counts. In mathematical terms Bachelier's achievement was to introduce many of the concepts of what is now known as stochastic analysis. His purpose, however, was to give a theory for the valuation of financial options. He came up with a formula that is both correct on its own terms and surprisingly close to the Nobel Prize-winning solution to the option pricing problem by Fischer Black, Myron Scholes, and Robert Merton in 1973, the first decisive advance since 1900.

Aside from providing an accurate and accessible translation, this book traces the twin-track intellectual history of stochastic analysis and financial economics, starting with Bachelier in 1900 and ending in the 1980s when the theory of option pricing was substantially complete. The story is a curious one. The economic side of Bachelier's work was ignored until its rediscovery by financial economists more than fifty years later. The results were spectacular: within twenty-five years the whole theory was worked out, and a multibillion-dollar global industry of option trading had emerged.


Mathematical and other scientific research can sometimes have a beauty akin to artistic masterworks. And, rarely, romance can even arise in how science progresses. One notable example of this is the 1914 discovery by the eminent British mathematician, G. H. Hardy, of the unknown mathematical genius Ramanujan—what Hardy called the greatest romance in his professional life.

That story began when the morning post brought to Trinity College, Cambridge, a letter from an unknown impoverished Madras clerk. Instead of giving it a cursory glance, Hardy examined with amazement the several enclosed infinite series. In a flash, he realized they were the work of a genius: a few Hardy already knew; maybe at least one was imperfect; but several were so novel that no mere talent could have discovered them. No need here to rehash the story of the Ramanujan–Hardy collaboration and the tragic early death from tuberculosis of Ramanujan.

As told in the preface below, discovery or rediscovery of Louis Bachelier’s 1900 Sorbonne thesis, ‘Théorie de la spéculation’, began only in the middle of the twentieth century, and initially involved a dozen or so postcards sent out from Yale by the late Jimmie Savage, a pioneer in bringing back into fashion statistical use of Bayesian probabilities. In paraphrase, the postcard’s message said, approximately, ‘Do any of you economist guys know about a 1914 French book on the theory of speculation by some French professor named Bachelier?’

Apparently I was the only fish to respond to Savage’s cast. The good MIT mathematical library did not possess Savage’s 1914 reference. But it did have something better, namely Bachelier’s original thesis itself.

I rapidly spread the news of the Bachelier gem among early finance theorists. And when our MIT PhD Paul Cootner edited his collection of worthy finance papers, on my suggestion he included an English version of Bachelier’s 1900 French text. I salute Davis and Etheridge for their present definitive translation, augmented by their splendid commentaries.

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