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 98 and a 1-year bond paying an 8% coupon semi-annually is priced at USD 103, using a replication approach, what should be the price of a 1-year Treasury bond that pays a coupon of 6% semiannually?

选项：

A.

USD 99.3

B.

USD 101.11

C.

USD 101.8

D.

USD 103.9

解释：

中文解析：

C正确。下面三个式子表示复制资产组合的现金流：

0时刻: 98*F1 + 103*F2 = F3 …………………………… 等式 (1)

0.5时刻: 0*F1 + 4*F2 = 3...……………………………. 等式 (2)

1时刻: 100*F1 + 104*F2 = 103 …………………... 等式 (3)

从等式2可知：F2 = 0.75.

代入等式3，可得F1=0.25.

将F1和F2代入等式1，可得F3= 98*0.25 + 103*0.75= 101.75.

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 8% coupon bond, respectively, corresponding to the proportions of the zero-coupon bond and the 8% 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 = 3/4 = 0.75

Substituting the value of F2 in Equation (3): 100*F1 + 104*0.75 = 103, giving, F1 = 0.25

Plugging the values of F1 and F2 in Equation (1), we determine F3 = 98*0.25 + 103*0.75 = 101.75