410140980 · 2021年10月13日
NO.PZ2016022702000004
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
Using the one- and two-year spot rates. we have
so
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%
老师问下spot rate和forward rate哪个可以近似理解为边际利率哪个是平均利率
NO.PZ2016022702000004 问题如下 A one-yezero-coupon bonyiel 4.0%. The two- anthree-yezero-coupon bon yiel5.0% an6.0% respectively.The rate for a one-yelobeginning in one yeis closest to: A.4.5% B.5.0%. C.6.0%. C is correct.From the forwarrate mol. we have[1+r(2)]2=[1+r(1)]1[1+f(1,1)]1{\lbrack1+r{(2)}\rbrack}^2={\lbrack{1+r(1)}\rbrack}^1{\lbrack{1+f(1,1)}\rbrack}^1[1+r(2)]2=[1+r(1)]1[1+f(1,1)]1Using the one- antwo-yespot rates. we have (1+0.05)2=(1+0.04)1[1+f(1,1)]1{(1+0.05)}^2={(1+0.04)}^1{\lbrack{1+f(1,1)}\rbrack}^1(1+0.05)2=(1+0.04)1[1+f(1,1)]1so (1+0.05)2(1+0.04)1−1=f(1,1)=6.010%\frac{{(1+0.05)}^2}{{(1+0.04)}^1}-1=f(1,1)=6.010\%(1+0.04)1(1+0.05)2−1=f(1,1)=6.010%考点通过spot rate计算forwarrate通过forwarrate mol，将一年期和两年期的spot rate代入上式，可以得到f(1,1)=6.010% 请问这个公式有什么错误？
请问这道题用不用先用Prate算Spot rate呢？
