Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae 2010th Edition-Wow! eBook

Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae 2010th Edition book cover

Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae 2010th Edition

Author(s): Christophe Profeta (Author), Bernard Roynette (Author), Marc Yor (Author)

Publisher: Springer
Publication Date: 12 Feb. 2010
Edition: 2010th
Language: English
Print length: 291 pages
ISBN-10: 9783642103940
ISBN-13: 9783642103940

Book Description

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 ? ?

Editorial Reviews

From the Back Cover

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.

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Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae 2010th Edition

Book Description

Editorial Reviews

From the Back Cover

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