Lecture #9: Black-Scholes option pricing formula
· Brownian Motion
The first formal mathematical model of financial asset prices, developed by Bachelier (1900), was the continuous-time random walk, or Brownian motion. This continuous-time process is closely related to the discrete-time versions of the random walk.
· The discrete-time random walk
Pk = Pk-1 + k,   k =  (-) with probability  (1-), P0 is fixed. Consider the following continuous time process Pn(t), t  [0, T], wh ...