YTM和Spot Rate

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 forward rate for a two-year loan begining in one year is closest to:

选项：

A.

5.0%

B.

6.0%

C.

7.0%

解释：

C is correct.

From the forward rate model.

${\lbrack{1+r(3)}\rbrack}^3={\lbrack{1+r(1)}\rbrack}^1{\lbrack{1+f(1,2)}\rbrack}^2$

Using the one and three-year spot rates. we find

${({1+0.06)}}^3={({1+0.04)}}^1{\lbrack{1+f(1,2)}\rbrack}^2$, so $\sqrt{\frac{{(1+0.06)}^3}{{(1+0.04)}^1}}-1=f(1,2)=7.014\%$

考点：通过spot rate计算forward rate

通过forward rate model，将一年期和三年期的spot rate代入上式，可以得到f(1,2)=7.014%