a. Prove that it is never optimal to exercise early (is, before maturity) an American call on a nondividend paying stock. What 'goes wrong' in your proof if you were to have a dividend paying stock? [5 marks] b. Consider a riskfree zero-coupon bond that matures at t = 2 with a face value of 100. lts prices at t = {0, 1} and the nal payoff at. t : 2 are as shown below. a @ L22 100 96.15 C 90.49 C 100 94.34 t and face value 100, so using this notation 19(0, 2) = 90.49. (1') What are the single-period riskfree interest rates implied by the bond prices? What is the t z 0 price of a risk-free zerocoupon bond maturing at t = 1, i.e., P(0,1). [6' marks] (ii) Corisider a potable bond with maturity t : 2, face value .8100 and no coupons. The putable bond has the identifying feature that the buyer of the bond has the right (but no obligation) to sell it back to the issuer for some predetermined price If at t = 1. Determine the optimal policy of the buyer of such a bond at t = 1 and its price at t z 0, PM\