老师想问下S1S2S3

问题如下：

A 3-year bond offers a 10% coupon rate with interest paid annually. Assuming the following sequence of spot rates, the price of the bond is closest to:

选项：

96.98.

101.46.

102.95.

解释：

B is correct.

The bond price is closest to 101.46. The price is determined in the following manner:

$PV=\frac{PMT}{{(1+Z_1)}^1}+\frac{PMT}{{(1+Z_2)}^2}+\frac{PMT+FV}{{(1+Z_3)}^3}$

$PV=\frac{10}{1+0.08}+\frac{10}{\left(1+0.09\right)^2}+\frac{10+100}{\left(1+0.095\right)^3}$

PV = 9.26 + 8.42 + 83.78 = 101.46

考点：Pricing Bonds with Spot Rates

解析：通过未来现金流折现求和，第一年的现金流(10)用S1折现，第二年的现金流(10)用S2折现，第三年的现金流(100+10)用S3折现，可得债券价格为101.46，故选项B正确。