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Alfred · 2024年05月10日

这两道题题干相同，答案怎么不一样

  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

相同的题目编号，NO.PZ201712110200000304

这道题的题解解释：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.

t=0时刻也能call

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1 个答案

pzqa31 · 2024年05月11日

嗨，努力学习的PZer你好：


同学你问的是这个吗https://class.pzacademy.com/qa/10667，这两道题答案都是C0.3443，是一样的，同学是哪里有疑问？

----------------------------------------------
努力的时光都是限量版，加油！

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NO.PZ2018123101000086 问题如下 Exhibit 1 shows par, spot, anone-yeforwarrates.Bon4 is a fixeRate Bon of Alpha Corporation, with 1.55% annucoupon ancallable pwithout any lockout perio. The bonmaturity is 3 years.Baseon the information above, the value of the embeeoption in Bon4 is closest to: A.nil. B.0.1906. C.0.8789. 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 bon= value of straight bon– value of call option on bon此，Embeecall option的价值为Value of call option on bon= Value of straight bon– Value of callable bon用Spot rate对该Straight bon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(1.0100)11.55​+(1.012012)21.55​+(1.012515)3101.55​=100.8789无赎回保护期的可赎回债券的价值不能超过100，因此call option的价值为=100.8789–100=0.8789。 解析里Call option的Value是100.8789-100=0.8789，但是提问中回答是100.8789-100.5446=0.3343，哪种算法才是正确的呢？

2024-06-23 12:09 1 · 回答

NO.PZ2018123101000086 问题如下 Exhibit 1 shows par, spot, anone-yeforwarrates.Bon4 is a fixeRate Bon of Alpha Corporation, with 1.55% annucoupon ancallable pwithout any lockout perio. The bonmaturity is 3 years.Baseon the information above, the value of the embeeoption in Bon4 is closest to: A.nil. B.0.1906. C.0.3343. 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 bon= value of straight bon– value of call option on bon此，Embeecall option的价值为Value of call option on bon= Value of straight bon– Value of callable bon用Spot rate对该Straight bon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(1.0100)11.55​+(1.012012)21.55​+(1.012515)3101.55​=100.8789而Callable bon定价需要使用1-yeforwarrate，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Forwarrate对Callable bon行定价因此Call option的Value为100.8789-100.5446=0.3343 老师，二叉树求债券时，二叉树的利率都是forwarrate对吗？

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2024-03-12 22:19 4 · 回答

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2024-01-23 22:26 1 · 回答