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Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae - Couverture souple

Livre 36 sur 53: Springer Finance

Profeta, Christophe; Roynette, Bernard; Yor, Marc

 
9783642103940: Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae
Couverture souple
ISBN 10 : 3642103944 ISBN 13 : 9783642103940
Editeur : Springer, 2010

Synopsis

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 ? ?

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de la quatrième de couverture

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer
Date d'édition
2010
Langue
anglais
ISBN 10 
3642103944
ISBN 13 
9783642103940
Reliure
Broché
Numéro d'édition
1
Nombre de pages
270
Coordonnées du fabricant
non disponible
Personne responsable
non disponible