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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Option Prices as Probabilities: A New Look at Generalized Black-Scholes Formulae

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

Profeta, Christophe
Yor, Marc
Roynette, Bernard

Paperback

Investing & FinanceGeneral MathematicsProbability & Statistics

ISBN10: 3642103944
ISBN13: 9783642103940
Publisher: Springer
Published: Feb 12 2010
Pages: 270
Weight: 0.90
Height: 0.70 Width: 6.00 Depth: 9.00
Language: English
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 ? ?

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