Let X; = at + 0'31, with some constants ,u and o, and the stock price be given by St = ext (a) Derive the stochastic differential equation for 5;. (b) Show that percentage price changes SJSR for u -=: t are independent of 3,, r 3' n. (c) Give the mean and the variance of St. Hint: use the moment generating function of Normal distribution. (d) Give the values of a for which the process S; is a martingale, and show why it is a martingale. Hint: use martingale property of stochastic integral. (e) Calculate the mean and the variance of the stochastic integral fT ei+3i [33