Exercise 4 [Forward on stock paying dividends]. Suppose a stock with price (8:) 20 pays dividends at a known dividend yield q, expressed as a percentage of the stock price on a continually corn- pounded per annum basis. We will show that the forward price of this stock at time t with maturity T is given by so, T] = stei'W'\". (6) (i) Consider a portfolio A at time t consisting of e'qir' units of stock, with dividends all rein- vested in the stock. Show that at the value of this portfolio at time T equals 83-. (ii) Consider another portfolio B at time 1' consisting of one long forward contract with delivery price K plus it'ef'r'\"l cash. Show that the value of this portfolio at time T equals ST. (iii) Conciude that Ste\"(T' = VKU, T] +Ke"'T'\". (7) Let K: FU, T) and deduce (6]