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王昕彤 · 2022年05月02日

关于callable bond的计算

  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.

老师，我计算出的callable bond 的价值是1时点末的现金流=101.55/1.01=100.54，call option的价值=straight bond的价值-callable bond的价值=100.87-100.54，选项中没有，请老师解答一下

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1 个答案

pzqa015 · 2022年05月03日

嗨，从没放弃的小努力你好：


callable bond的价格有上限，不能超过100，所以，callable bond的value应该是100，而不应该是100.54哈。

如果callable bond的value是100，straight bond的value是100.8789，那么option value=0.8789。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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