Option Prices as Probabilities

0, P) - t t note a standard Brownian motion with B = 0, (F ,t? 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. Let N be the cumulative distribution function of a reduced Gaussian variable: x 2 y 1 ? 2 ? (t) and K C (t) in terms ofN : K ? (0.4) K t 2 t 2 and ?