Problem 5 (Digital options). (4 pts) A digital call option is a derivative security on an underlying stock S. If it has a strike K and maturity T, then the option will have a payoff at maturity given by 1, if ST >K, Digital Call Payoff 0, if ST K. (a) (1.5 pts) Draw the payoff at maturity of a portfolio X = DC + DP of one long digital call (DC) and one long digital put (DP) as a function of St. (b) (2.5 pts) If the price of a digital put today is Po, find the price today of the digital call Co. Assume the risk-free interest rate (with continuously compounding) is r