Option Prices as Probabilities

A New Look at Generalized Black-Scholes Formulae

  • Cristophe Profeta
  • Bernard Roynette
  • Marc Yor

Part of the Springer Finance book series (FINANCE)

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 1-20
  3. Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 21-63
  4. Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 65-87
  5. Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 89-113
  6. Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 115-141
  7. Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 143-159
  8. Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 161-201
  9. Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 203-237
  10. Back Matter
    Pages 239-270

About this book

Introduction

The Black-Scholes formula plays a central role in Mathematical Finance; it gives the right price at which buyer and seller can agree with, in the geometric Brownian framework, when strike K and maturity T are given. This yields an explicit well-known formula, obtained by Black and Scholes in 1973.

The present volume gives another representation of this formula in terms of Brownian last passages times, which, to our knowledge, has never been made in this sense.

The volume is devoted to various extensions and discussions of features and quantities stemming from the last passages times representation in the Brownian case such as: past-future martingales, last passage times up to a finite horizon, pseudo-inverses of processes... They are developed in eight chapters, with complements, appendices and exercises.

Keywords

Azéma supermartingale Black-Scholes Black-Scholes Formulae Finite Horizon Last passages times Martingale Pseudo-inverses

Authors and affiliations

  • Cristophe Profeta
    • 1
  • Bernard Roynette
    • 2
  • Marc Yor
    • 3
  1. 1.Inst. Élie Cartan (IECN)Université Nancy IVandoeuvre-les-Nancy CXFrance
  2. 2.Inst. Elie CartanUniversité Nancy IVandoeuvre-les-Nancy CXFrance
  3. 3.Labo. Probabilités et Modèles AléatoiresUniversité Paris VIParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-10395-7
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-10394-0
  • Online ISBN 978-3-642-10395-7
  • About this book