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Option Prices as Probabilities

A New Look at Generalized Black-Scholes Formulae

  • Book
  • © 2010

Overview

Authors:
  1. Cristophe Profeta

    1. Inst. Élie Cartan (IECN), Université Nancy I, Vandoeuvre-les-Nancy CX, France

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  2. Bernard Roynette

    1. Inst. Elie Cartan, Université Nancy I, Vandoeuvre-les-Nancy CX, France

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  3. Marc Yor

    1. Labo. Probabilités et Modèles Aléatoires, Université Paris VI, Paris, France

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  • To the best of our knowledge this book discusses in a unique way last passage times
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Finance (FINANCE)

Part of the book sub series: Springer Finance Lecture Notes (SFLN)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XXI
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  2. Reading the Black-Scholes Formula in Terms of First and Last Passage Times

    • Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 1-20

  3. Generalized Black-Scholes Formulae for Martingales, in Terms of Last Passage Times

    • Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 21-63

  4. Representation of some particular Azéma supermartingales

    • Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 65-87

  5. An Interesting Family of Black-Scholes Perpetuities

    • Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 89-113

  6. Study of Last Passage Times up to a Finite Horizon

    • Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 115-141

  7. Put Option as Joint Distribution Function in Strike and Maturity

    • Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 143-159

  8. Existence and Properties of Pseudo-Inverses for Bessel and Related Processes

    • Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 161-201

  9. Existence of Pseudo-Inverses for Diffusions

    • Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 203-237

  10. Back Matter

    Pages 239-270
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Keywords

About this book

Discovered in the seventies, Black-Scholes formula continues to play a central role in Mathematical Finance. We recall this formula. Let (B ,t? 0; F ,t? 0, P) - t t note a standard Brownian motion with B = 0, (F ,t? 0) being its natural ?ltra- 0 t t tion. Let E := exp B? ,t? 0 denote the exponential martingale associated t t 2 to (B ,t? 0). This martingale, also called geometric Brownian motion, is a model t to describe the evolution of prices of a risky asset. Let, for every K? 0: + ? (t) :=E (K?E ) (0.1) K t and + C (t) :=E (E?K) (0.2) K t denote respectively the price of a European put, resp. of a European call, associated with this martingale. Let N be the cumulative distribution function of a reduced Gaussian variable: x 2 y 1 ? 2 ? N (x) := e dy. (0.3) 2? ?? The celebrated Black-Scholes formula gives an explicit expression of? (t) and K C (t) in terms ofN : K ? ? log(K) t log(K) t ? (t)= KN ? + ?N ? ? (0.4) K t 2 t 2 and ? ?

Authors and Affiliations

  • Inst. Élie Cartan (IECN), Université Nancy I, Vandoeuvre-les-Nancy CX, France

    Cristophe Profeta

  • Inst. Elie Cartan, Université Nancy I, Vandoeuvre-les-Nancy CX, France

    Bernard Roynette

  • Labo. Probabilités et Modèles Aléatoires, Université Paris VI, Paris, France

    Marc Yor

Bibliographic Information

  • Book Title: Option Prices as Probabilities

  • Book Subtitle: A New Look at Generalized Black-Scholes Formulae

  • Authors: Cristophe Profeta, Bernard Roynette, Marc Yor

  • Series Title: Springer Finance

  • DOI: https://doi.org/10.1007/978-3-642-10395-7

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2010

  • Softcover ISBN: 978-3-642-10394-0Published: 12 February 2010

  • eBook ISBN: 978-3-642-10395-7Published: 26 January 2010

  • Series ISSN: 1616-0533

  • Series E-ISSN: 2195-0687

  • Edition Number: 1

  • Number of Pages: XXI, 270

  • Number of Illustrations: 3 b/w illustrations

  • Topics: Probability Theory and Stochastic Processes, Quantitative Finance

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