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小猫批脸 · 2021年06月23日

考试真的要考这种题吗，太复杂了计算。

  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

我一看就懵了，光写那些小数点还有按计算器就花不少时间。所以我把计算过程写了出来。。

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WallE_品职答疑助手 · 2021年06月23日

嗨，努力学习的PZer你好：


不会这么复杂，考试时间有限所以会出个简化版的，比如二叉树只有两期，但咱们平时必须把复杂版的都练会了 思路都整理清晰了才可以。

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努力的时光都是限量版，加油！

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