Exercise 4 (Forward on stock paying dividends). Suppose a stock with price (St) ezo pays dividends at a known dividend yield q, expressed as a percentage of the stock price on a continually com- pounded per annum basis. We will show that the forward price of this stock at time t with maturity T is given by F(t, T) = Ster-q)(T-0). (6) (1) Consider a portfolio A at time t consisting of e-7(7-6) units of stock, with dividends all rein- vested in the stock. Show that at the value of this portfolio at time T equals St. (ii) Consider another portfolio B at time t consisting of one long forward contract with delivery price K plus Ke e- (T-1) cash. Show that the value of this portfolio at time T equals St. (iii) Conclude that Ste-GT-1) = V((t, T) + Ke-r(T-t). (7) Let K = F(t,T) and deduce (6)