这道题怎么理解

问题如下：

Using the following US Treasury forward rates, the value of a 2.5-year $100 par value Treasury bond with a 5% coupon rate is closest to:

选项：

A.$104.87. B.$101.52. C.$106.83.

解释：

C is correct. The value of the bond is

$\begin{array}{l}\frac{2.5}{\left(1+0.012/2\right)}+\frac{2.5}{\left(1+0.012/2\right)\times \left(1+0.18/2\right)}+\\ \frac{2.5}{\left(1+0.012/2\right)\times \left(1+0.018/2\right)\times \left(1+0.023/2\right)}+\\ \frac{2.5}{\left(1+0.012/2\right)\times \left(1+0.018/2\right)\times \left(1+0.023/2\right)\times \left(1+0.027/2\right)}+\\ \frac{102.5}{\left(1+0.012/2\right)\times \left(1+0.018/2\right)\times \left(1+0.023/2\right)\times \left(1+0.027/2\right)\times \left(1+0.030/2\right)}=\$106.83\end{array}$

A is incorrect because it treats the forward rates as spot rates.

B is incorrect because it does not divide the forward rates by two.

考点：利用远期利率求债券价值

解析：通过未来现金流折现求和，可得债券价值为106.83。注意，债券半年付息一次，因此coupon rate和forward rate都需要去年化。