We consider a Brownian motion (Wt)t?[0,1].
(1) Compute the expectation and the variance of W1/2 + W1.
(2) We consider a Black-Scholes model such that the bond price is given by Bt= e.1t and the stock price is given by St = 100e.2t+.5Wt . What is the initial stock price?
What is the interest rate? What is the volatility?
(3) With the help of a table of normal distribution, give an approximation (with error at most 0.01) of the probability that the stock price is larger at time 1 than it is a at time 0.