Option Prices as Probabilities - A New Look at Generalized Black-Scholes Formulae (Paperback, Edition.)

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 ? ?

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Springer Finance
Release date:	February 2010
First published:	2010
Authors:	Christophe Profeta • Bernard Roynette • Marc Yor
Dimensions:	235 x 155 x 15mm (L x W x T)
Format:	Paperback
Pages:	270
Edition:	Edition.
ISBN-13:	978-3-642-10394-0
Categories:	Books > Business & Economics > Finance & accounting > General Books > Science & Mathematics > Mathematics > Probability & statistics
LSN:	3-642-10394-4
Barcode:	9783642103940

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