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Cooljas · 2024年04月27日

红框里是怎么取值算的啊,为啥要减去?还有d(0.5) d(1) d(1.5)的含义分别是什么?

NO.PZ2023091802000079

问题如下:

The table below gives coupon rates and mid-market price for three U.S. Treasury bonds for settlement on (as of) May 31, 2013

Which of the following is nearest to the implied discount function (set of discount factors) assuming semi-annual compounding?

选项:

A.

d(0.5) = 0.9370, d(1.0) = 0.8667, d(1.5) = 0.9210

B.

d(0.5) = 0.9920, d(1.0) = 0.9700, d(1.5) = 0.9350

C.

d(0.5) = 0.9999, d(1.0) = 0.7455, d(1.5) = 0.8018

D.

d(0.5) = 1.0350, d(1.0) = 1.1175, d(1.5) = 0.6487

解释:

The future value of $1 invested for time t is 1/d(t).



1 个答案

pzqa39 · 2024年04月28日

嗨,从没放弃的小努力你好:


d() 是折现因子

第一个债券到期半年 0.5

现在值100.626, 到期时会有coupon及100 面值, coupon rate 是 2+7/8,coupon=100 *(2+7/8)%/2 =1.4375

d(0.5 )= 100.626 / (100+ 1.4375) = 0.992


第二个债券 一年到期,能拿到2 个coupon,(0.5 时刻和1时刻)

Coupon= 100*2.5%/2=1.25

1.25 *d(0.5 )+(100+1.25)*d(1) = 99.45

代入d(0.5 ),d(1)=0.97


建议听一下经典题,section 19, bond valuation 中有详细讲解

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