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

byChristophe Profeta, Bernard Roynette, Marc Yor

Paperback | February 12, 2010

Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae by Christophe Profeta
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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 ? ?
Title:Option Prices as Probabilities: A New Look at Generalized Black-Scholes FormulaeFormat:PaperbackProduct dimensions:270 pages, 9.25 X 6.1 X 0 inShipping dimensions:270 pages, 9.25 X 6.1 X 0 inPublished:February 12, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3642103944

ISBN - 13:9783642103940

Appropriate for ages: All ages

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