Part I. (a). Explain why an American call options on futures could be optimally exercised early while call options on the spot cannot be optimally exercised. Assume that there is no dividend. (b). Explain that an at-the-money call option on a given stock must cost more than an at-the-money put option on that stock with the same maturity. The stock will pay no dividends until after the expiration data. Part II. Consider a five-year bond with a 10% coupon, paid every six-months and with yield-to-maturity 8% per annum semi-annual compounding. If the bonds yield-to-maturity remains constant, then in one year, will the bond price be higher, lower, or unchanged? Please justify your answer.