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Luhunlu · 2022年06月26日

老师，请问callable bond value为什么是100？

  1. CFA II
  2. Fixed Income

* 问题详情，请 查看题干

NO.PZ201712110200000304

问题如下：

Based on the information in Exhibit 1 and Exhibit 2, the value of the embedded option in Bond 4 is closest to:

选项：

A.

nil.

B.

0.1906.

C.

0.8789.

解释：

C is correct.

Bond 4 is a callable bond. Value of an issuer call option = Value of straight bond – Value of callable bond. The value of the straight bond may be calculated using the spot rates or the one-year forward rates.

Value of an option-free (straight) bond with a 1.55% coupon using spot rates:

1.55/(1.0100)1 + 1.55/(1.012012)2 + 101.55/(1.012515)3 = 100.8789.

The value of a callable bond (at par) with no call protection period cannot exceed 100, as at that price or higher the bond would be called. The value of the call option = 100.8789 – 100 = 0.8789.

不是应该用二叉树来算吗？是题目中没有给出二叉树就按照100来做吗？我是用题目下面给出的二叉树算的，但是并没有相应的选项

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1 个答案

pzqa015 · 2022年06月28日

嗨，爱思考的PZer你好：


题目让用表1和表2 来计算，所以，不能用表3的二叉树。

题目让计算value of call option，根据Vcallable=Voption free-V calloption，

就要先计算Vcallable 与V option free。

Voption free是不含权债，就用spot rate来折现。而Vcallable是callable bond，它的价格不会超过100（一般我们都认为callable bond的call price是100，如果超过100，就会被call回，所以它的price最多为100）。

有了这两个值，就可以计算得到Vcall option。


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