Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae (Springer Finance)

Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae (Springer Finance) Summary:

By Cristophe Profeta, Bernard Roynette, Marc Yor

Publisher:   Springer

Number Of Pages:   250

Publication Date:   2010-02-01

ISBN-10 / ASIN:   3642103944

ISBN-13 / EAN:   9783642103940

Product Description:

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 ever 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.

Table of Contents: Chapter 1: Reading the Black-Scholes Formula in Terms of First and Last Passage Times Chapter 2: Generalized Black-Scholes Formulae for Martingales, in Terms of Last Passage Times Chapter 3: Representation of some particular Azéma supermartingales Chapter 4: An Interesting Family of Black-Scholes Perpetuities Chapter 5: Study of Last Passage Times up to a Finite Horizon Chapter 6: Put Option as Joint Distribution Function in Strike and Maturity Chapter 7: Existence and Properties of Pseudo-Inverses for Bessel and Related Processes Chapter 8: Existence of Pseudo-Inverses for Diffusions  

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