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Taschenbuch. Zustand: Neu. Neuware -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 Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 292 pp. Englisch.

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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.