Logo - springer
Slogan - springer

Mathematics - Probability Theory and Stochastic Processes | Option Prices as Probabilities - A New Look at Generalized Black-Scholes Formulae

Option Prices as Probabilities

A New Look at Generalized Black-Scholes Formulae

Profeta, Christophe, Roynette, Bernard, Yor, Marc

2010, XXI, 270 p. 3 illus.

Available Formats:

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.


(net) price for USA

ISBN 978-3-642-10395-7

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase

learn more about Springer eBooks

add to marked items


Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.


(net) price for USA

ISBN 978-3-642-10394-0

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days

add to marked items

  • To the best of our knowledge this book discusses in a unique way last passage times

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.

Content Level » Research

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

Related subjects » Probability Theory and Stochastic Processes - Quantitative Finance

Table of contents / Sample pages 

Reading the Black-Scholes Formula in Terms of First and Last Passage Times.- Generalized Black-Scholes Formulae for Martingales, in Terms of Last Passage Times.- Representation of some particular Azéma supermartingales.- An Interesting Family of Black-Scholes Perpetuities.- Study of Last Passage Times up to a Finite Horizon.- Put Option as Joint Distribution Function in Strike and Maturity.- Existence and Properties of Pseudo-Inverses for Bessel and Related Processes.- Existence of Pseudo-Inverses for Diffusions.

Popular Content within this publication 



Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Probability Theory and Stochastic Processes.