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Louis Bachelier's Theory of Speculation

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

Mark Davis
Alison Etheridge
Copyright Date: 2006
Pages: 192
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  • Book Info
    Louis Bachelier's Theory of Speculation
    Book Description:

    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 thesisThéorie de la Spéculationat 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.

    eISBN: 978-1-4008-2930-9
    Subjects: Finance, Mathematics

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-vi)
  3. Foreword
    (pp. vii-xii)
    Paul A. Samuelson

    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...

  4. Preface
    (pp. xiii-xvi)
    Mark Davis and Alison Etheridge
  5. CHAPTER ONE Mathematics and Finance
    (pp. 1-14)

    ‘Janice! D’ya think you can find that postcard?’

    Professor Paul A. Samuelson was in his office at MIT in the Autumn of 2003 relating how, several decades earlier, he had come across the PhD thesis, dating back to 1900, in which Louis Bachelier had developed a theory of option pricing, a topic that was beginning to occupy Samuelson and other economists in the 1950s. Although no economist at the time had ever heard of Bachelier, he was known in mathematical circles for having independently invented Brownian motion and proved some results about it that appeared in contemporary texts such as...

  6. CHAPTER TWO Théorie de la Spéculation
    (pp. 15-79)

    The influences that determine the movements of the Exchange are innumerable; past, current and even anticipated events that often have no obvious connection with its changes have repercussions for the price. Alongside the, as it were, natural variations, artificial causes also intervene: the Exchange reacts to itself and the current movement is a function not only of previous movements but also of the current state. The determination of these movements depends upon an infinite number of factors; it is thus impossible to hope for mathematical predictability. Contradictory opinions about these variations are so divided that at the same time the...

  7. CHAPTER THREE From Bachelier to Kreps, Harrison and Pliska
    (pp. 80-115)

    Bachelier gained his mathematics degree at the Sorbonne in 1895. He studied under an impressive lineup of professors including Paul Appell, Emile Picard, Joseph Boussinesq and Henri Poincaré.

    Appell was a prodigious problem solver with little taste for developing general theories, and although he gave his name to a sequence of polynomials, his numerous contributions to analysis, geometry and mechanics are little remembered today. Picard’s name, by contrast, is familiar to any undergraduate mathematician. It is attached to theorems in analysis, function theory, differential equations and analytic geometry. He also had the reputation for being an excellent teacher. In his...

  8. CHAPTER FOUR Facsimile of Bachelier’s Original Thesis
    (pp. 116-182)

    On the following pages you will find a facsimile of Bachelier’s original thesis, first published in 1900 inAnnales Scientifique de l’École Normale Supérieure, 3esérie, tome 17, pp. 21–86.

    This is reprinted here with the permission of École Normale Supérieure de Paris and was scanned for this publication by the Cambridge University Library.

    Les influences qui déterminent les mouvements de la Boursc sont innombrables, des événements passés, actuels ou méme escomptables, ne présentant souvent aucun rapport apparent avec ses variations, se répercutent sur son cours.

    A côté des causes en quelque sorte naturelles des variations, interviennent aussi des...

  9. References
    (pp. 183-189)