uncertainty of the expected inflation不是针对长期的债券么？为什么这题一年的短期债券也要算这个？

问题如下：

2. The implied premium for inflation uncertainty for the one-year government zero-coupon bond proposed by Carlisle is closest to:

选项：

0.23%.

0.37%.

1.10%.

解释：

B is correct.

The pricing equation for a default-free nominal coupon-paying bond is

$P_t^i=\sum_{s=1}^N\frac{CF_{t+s}^i}{{(1+l_{t,s}+\theta_{t,s}+\pi_{t,s}^i)}^s}$

For a one-year bond, the pricing formula reduces to

$P_t^{}=\frac{CF_{t+s}^{}}{{(1+l_{t,1}+\theta_{t,1}+\pi_{t,1}^{})}^s}$

Thus, the implied premium for inflation uncertainty for the one-year government zero-coupon bond is calculated as$begin{array}{l}\Pi_{\text{t},1}=\frac{CF_{t+1}}{P_t}-(1+l_{t,1}+\theta_{t,1})\\=\frac{100}{96.37}\text{-}{(1\text{ }+\text{ }0.0115\text{ }+\text{ }0.0225)}\\=\text{ }1.0377\text{ - }1.0340\\=\text{ }0.0037,\text{ }or\text{ }0.37\%$

考点： one-year default-free zero-coupon bond

解析：未来现金流折现求和计算债券价格。已知价格，折现率包括 real risk-free rate，expects inflation，inflation uncertainty ，没有违约风险所以没有credit spread。求inflation uncertainty，代入数值计算即可。