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西红柿面 · 2024年04月09日

callable bond的价格有上限，不能超过100，所以，callable bond的value应该是100

  1. CFA II
  2. Fixed Income

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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.

callable bond的价格有上限，不能超过100，所以，callable bond的value应该是100，这句话怎么理解呢

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吴昊_品职助教 · 2024年04月10日

嗨，从没放弃的小努力你好：


不含权债券在利率下降的时候，价格上涨。callable bond在利率下降的时候，债券发行人会提前以call price赎回债券，因此，callable bond在利率下降的时候价格涨不上去，一旦超过call price，发行人就会赎回债券。价格存在一个上限，这个上限就是call price。

债券4是callable at par，说明执行价格就是100，100就是价格上限，不能超过100。

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