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Jayden · 2021年01月09日

问一道题:NO.PZ2018123101000002

问题如下:

Spot curve shows: r(1) = 3.5%, r(2) = 4.5%, and r(3) = 5.6%. According to the spot rates, the forward rate for a one-year loan beginning in one year will be:

选项:

A.

less than the forward rate for a one-year loan beginning in two-years.

B.

greater than the forward rate for a two-year loan beginning in one-year.

C.

greater than the forward rate for a one-year loan beginning in two-years.

解释:

A is correct.

考点:通过Spot rate计算Forward rate

解析:

通过Spot rate计算Forward rate的公式,从第1年末开始的一年期Forward rate为:

(1+S2)2=(1+S1)(1+f(1,1))1{(1+S_2)}^2=(1+S_1){(1+f(1,1))}^1;代入数据,可得f(1,1)为: 5.51%;

对于A选项f(2,1)为:

(1+S3)3=(1+S2)2(1+f(2,1))1{(1+S_3)}^3={(1+S_2)}^2{(1+f(2,1))}^1;代入数据,可得f(2,1)为: 7.84%

因此A选项正确;C选项错误;

对于B选项f(1,2)为:

f(1,2)2×(1+3.5%)=(1+5.6%)3f(1,2)^2\times(1+3.5\%)=(1+5.6\%)^3

可算的f(1,2)=6.7%,因此B选项错误。

算f(1,1)时,能不能用 (1.045)^2 * (1+f(1,1)) = (1.056)^3 => f(1,1)=7.83%,为何这样算不行? 

1 个答案
已采纳答案

吴昊_品职助教 · 2021年01月09日

同学你好:

你想通过S2和S3得到的远期利率,并不是f(1,1),而是f(2,1)。

一次性投资两年,然后站在第二年末再投资一年f(2,1),和一次性投资三年,应该是等效的。