Suppose that a stock price S follows geometric Brownian motion with ex- pected return and volatility : dS = Sdt + Sdz.

Suppose that in the first two years = 2 and = 3 and for the next two years = 3 and = 4. If the initial value of the variable is S0 =2andn=1find: i. the expected value of S and F = Sn after two years;

ii. the probability distribution of f2 f0;

iii. the probability distribution of f4 f0;

iv. the probability distribution of f4.