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... more...