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huangme7 · 2022年06月08日

不明白 为什么 call at 100

  1. CFA II
  2. Fixed Income

NO.PZ2018123101000086

问题如下：

Exhibit 1 shows par, spot, and one-year forward rates.

Bond 4 is a fixed-Rate Bonds of Alpha Corporation, with 1.55% annual coupon and callable at par without any lockout periods. The bond maturity is 3 years.

Based on the information above, the value of the embedded option in Bond 4 is closest to:

选项：

A.

nil.

B.

0.1906.

C.

0.3343.

解释：

C is correct.

考点：考察对含权债券的理解

解析：

债券4是可Callable。其价值为：

Value of callable bond = value of straight bond – value of call option on bond

因此，Embedded call option的价值为：

Value of call option on bond = Value of straight bond – Value of callable bond

利用Spot rate对该Straight bond进行定价为：

1.55(1.0100)1+1.55(1.012012)2+101.55(1.012515)3=100.8789\frac{1.55}{{(1.0100)}^1}+\frac{1.55}{{(1.012012)}^2}+\frac{101.55}{{(1.012515)}^3}=100.8789

而Callable bond的定价需要使用1-year forward rate，将债券的现金流从最后一期开始，依次向前一个节点折现，以判断折现值是否会触发行权价；使用表格中的Forward rate对Callable bond进行定价：

因此Call option的Value为：100.8789-100.5446=0.3343

不明白 为什么 call at 100。当前100.5446， 这个值> 100, 那就是现在就召回了， 也能不到year 1，year 2 了。

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1 个答案

pzqa015 · 2022年06月08日

嗨，爱思考的PZer你好：


一般我们假定callable bond的call price是100元，对于callable bond，可以行权后，它的价格不能超过call price100元。

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