老师，为什么不能用（1+s1)(1+f1,1)^2=(1+s3)^3来算？

问题如下：

A one-year zero-coupon bond yields 4.0%. The two- and three-year zero-coupon bonds yield 5.0% and 6.0% respectively.

The rate for a one-year loan beginning in one year is closest to:

选项：

A.

4.5%

B.

5.0%.

C.

6.0%.

解释：

C is correct.

From the forward rate model. we have

${\lbrack1+r{(2)}\rbrack}^2={\lbrack{1+r(1)}\rbrack}^1{\lbrack{1+f(1,1)}\rbrack}^1$

Using the one- and two-year spot rates. we have

${(1+0.05)}^2={(1+0.04)}^1{\lbrack{1+f(1,1)}\rbrack}^1$so $\frac{{(1+0.05)}^2}{{(1+0.04)}^1}-1=f(1,1)=6.010\%$

考点：通过spot rate计算forward rate

$$

通过forward rate model，将一年期和两年期的spot rate代入上式，可以得到f(1,1)=6.010%