Question 3 (10 marks) Let F, the future price on a (non-dividend paying) stock, S, with time to maturity T - t be given as : F = Ser(T - t), r is interest rate, t, time, T, terminal time. Also assume that the stock price dS/S follows a standard geometric Brownian motion (GBM) dS = (us)dt + oSdz (a) Show all the steps in your derivations. What is the process followed by S2? Does this process follow a GBM? What is the mean and the variance rate of the new process? (5 marks) (b) Show all the steps in your derivations. Show that dF/F follows a GBM with drift rate u - r and variance o2. (5 marks) Question 3 (10 marks) Let F, the future price on a (non-dividend paying) stock, S, with time to maturity T - t be given as : F = Ser(T - t), r is interest rate, t, time, T, terminal time. Also assume that the stock price dS/S follows a standard geometric Brownian motion (GBM) dS = (us)dt + oSdz (a) Show all the steps in your derivations. What is the process followed by S2? Does this process follow a GBM? What is the mean and the variance rate of the new process? (5 marks) (b) Show all the steps in your derivations. Show that dF/F follows a GBM with drift rate u - r and variance o2