求解释。。。。

问题如下：

An analyst has 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 97 and a 1-year 7% coupon bond with semi-annual payments is priced at USD 102, using a replication approach, what should be the price of a 1-year 6% coupon Treasury bond that pays semi-annually?

选项：

A.

USD 97.71

B.

USD 101.04

C.

USD 101.29

D.

USD 102.86

解释：

中文解析：

下面三个式子表示复制资产组合的现金流：

0时刻: 97*F1 + 102*F2 = F3 …………………………… 等式 (1)

0.5时刻: 0*F1 + 3.5*F2 = 3...……………………………. 等式 (2)

1时刻: 100*F1 + 103.5*F2 = 103 …………………... 等式 (3)

从等式2可知：F2 = 0.8571 .

代入等式3，可得F1=0.1429

将F1和F2代入等式1，可得F3 = 97*0.1429 + 102*0.8571 = 101.2855 .

To determine the price (F3) of the 6% coupon bond by replication, where F1 and F2 are the weight factors in the replicating portfolio for the zero-coupon bond and the 7% coupon bond, respectively, corresponding to the proportions of the zero-coupon bond and the 7% coupon bond to be held, and given a 1-year horizon:

The three equations below express the requirement that the cash flows of the replicating portfolio, on each cash flow date (t, in years), be equal to the cash flow of the 6% coupon bond:

From Equation (2), F2 = 3/3.5 = 0.8571

Substituting the value of F2 in Equation (3): 100*F1 + 103.5*0.8571 = 103, giving, F1 = 0.1429

Plugging the values of F1 and F2 in Equation (1), we determine F3 = 97*0.1429 + 102*0.8571 = 101.2855

A is incorrect. USD 97.71 is the price of the 1-year 6% coupon Treasury bond if the weight factors, F1 and F2, are switched in Equation (1).

B is incorrect. USD 101.04 is the price of the 1-year 6% coupon Treasury bond if the yield-to-maturity of the 1-year 7% coupon Treasury bond is used in its pricing and the zero-coupon Treasury bond is ignored.

D is incorrect. USD 102.86 is the price of the 1-year 6% coupon Treasury bond if the yield-to-maturity of the zero-coupon Treasury bond is used in its pricing and the 1-year 7% coupon Treasury bond is ignored.