Consider a stock whose price has the volatility and drift , and at time, is given by the geometric Brownian motion:

S(t) = S(0)exp{( 0.5^2)t + W(t)}

where W(t) is a standard Brownian motion. Consider a Binomial model with N periods, with each period of length T= T/N units of time, and with

u= 1 +T + (T)

d= 1 +T(T)

Show that the price of the stock on the binomial tree at period N approaches the random variable S(T) as N.