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徐威廉 · 2020年08月09日

问一道题：NO.PZ2018123101000086 [ CFA II ]

  1. CFA II
  2. Fixed Income

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

看了解答，还是不明白为什么含权债卷直接用forward rate折现，我的思路是用第三行的条件既S3和S1求出S2后折现，但是答案相差很远
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WallE_品职答疑助手 · 2020年08月09日

同学你好，

这答案中不知道您注意了没

“利用Spot rate对该Straight bond进行定价”

“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”

对于不含权债券，我们是用spot rate直接折现。

对于含权的，我们只能从后往前一期一期的折现，注意是一期一期，这就不能用s2，s3之类的了。因为我们需要判断每期是否会被行权。

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