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柚柚_柚 · 2021年08月30日

答案错了吧 

  1. CFA II
  2. Fixed Income

NO.PZ2018123101000091

问题如下：

Note: Each bond has a remaining maturity of three years, annual coupon payments, and a credit rating of BBB.

Bianchi constructs binomial interest rate tree based on a 10% interest rate volatility assumption and a current one-year rate of 1%. Panel A of Exhibit 2 provides an interest rate tree assuming the benchmark yield curve shifts down by 30 bps. Panel B provides an interest rate tree assuming the benchmark yield curve shifts up by 30 bps.

Bianchi determines that the AI bond is currently trading at an option-adjusted spread (OAS) of 13.95 bps relative to the benchmark yield curve.

Based on Exhibits 1 and 2, the effective duration for the AI bond is closest to:

选项：

A.

1.98.

B.

2.15

C.

2.73

解释：

B is correct.

考点：考察Effective duration的计算

解析：

本题的计算比较多，需要利用利率向上平移的二叉树计算出PV(+)，并且利用利率向下平移的二叉树计算出PV(-)。PV0为100.200为表一中已知信息。

利率向下平移30 bps，债券价格 (PV – ) 为100.78.

利率向上平移30 bps，债券价格(PV+) 为99.487.

利用Effective duration公式有：

ED=(PV−)−(PV+)2×(ΔCurve)×(PV0)=100.780−99.4872×0.003×100.200=2.15ED=\frac{(PV_-)-(PV_+)}{2\times(\Delta Curve)\times(PV_0)}=\frac{100.780-99.487}{2\times0.003\times100.200}=2.15

在下面加30bps的第一个down节点 不应该是赎回用面值吗 都小于5.25%
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4 个答案

潘吖吖 · 2022年02月26日

我也觉得4.9377那个节点是错的？



WallE_品职答疑助手 · 2021年09月02日

嗨，从没放弃的小努力你好：


callable at par的意思是 超过面值100的时候才会被行权 从第二年折现到第一年的下端value是小于100的 所以不用行权。


债券被不被call 既不是基于coupon rate 也不是基于par rate，是基于债券的价格/价值和行权价。



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虽然现在很辛苦，但努力过的感觉真的很好，加油！

WallE_品职答疑助手 · 2021年08月31日

嗨，爱思考的PZer你好：


麻烦同学把你认为应该怎么计算的过程写出来。您说的话我真的是不太理解 。不好意思啊，因为我从来没听过“用coupon rate对应的spot”这种说法。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

柚柚_柚 · 2021年08月31日

就是这个答案用错折现率了.... 今天考试了不写了😂

柚柚_柚 · 2021年09月01日

不是，之前是手机打字不好说，coupon不是call at par，这个u1d节点用的折现率都低于par rate了明显是错的啊？

WallE_品职答疑助手 · 2021年08月30日

嗨，从没放弃的小努力你好：


我没明白你的意思，你是指99.711这个节点为什么没被行权？ 行权价是100 是基于行权价赎回，不是基于coupon rate 赎回

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

柚柚_柚 · 2021年08月30日

4.9377%的节点计算是错的 ，小于coupon应该用coupon rate对应的spot吧

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