题目
You have been asked to check for arbitrage opportunities in the Treasury bond market by comparing the cash flows of selected bonds with the cash flows of combinations of other bonds. If a 1-year zero-coupon bond is priced at USD 96.12 and a 1-year bond paying a 10% coupon semi-annually is priced at USD 106.20, what should be the price of a 1-year Treasury bond that pays a coupon of 8% semiannually?
选项
A.USD 98.10
B.USD 101.23
C.USD 103.35
D.USD 104.18
答案
D
解析
The solution is to replicate the 1 year 8% bond using the other two treasury bonds. In order to replicate the cash flows of the 8% bond, you could solve a system of equations to determine the weight factors, Fl and F2, which correspond to the proportion of the zero and the 10% bond to be held, respectively.The two equations are as follows:(100 × F1) + (105 × F2) = 104 (replicating the cash flow including principal and interest payments at the end of 1 year), and (5 × F2) = 4 (replicating the cash flow from the coupon payment in 6 months.)Solving the two equations gives us Fl = 0.2 and F2 = 0.8. Thus the price of the 8% bond should be 0.2 (96.12) + 0.8 (106.2) = 104.18. 本题的解题思路是用其他的两个国债来复制1年期的8%的息票的债券，因此，8%的息票的债券的价格是0.2 × 96.12 0.8 × 106.20 = 104.184。