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xxxxsdadas · 2021年07月21日

从哪里看出来现在的价格100.2是合理价格

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：

$ED=\frac{(PV_-)-(PV_+)}{2\times(\Delta Curve)\times(PV_0)}=\frac{100.780-99.487}{2\times0.003\times100.200}=2.15$

该题二叉树计算过程是105.25向T0方向进行推导计算V+和V-，那算出来的是合理定价。在计算的过程中，一直对这个100.2是否为V0存疑。如何判断100.2就是合理定价？

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WallE_品职答疑助手 · 2021年07月24日

嗨，从没放弃的小努力你好：

理解您的思路，

但相信您也做过不少题目啦，并不是每一题的每个value或者价格都加上了 fair value这句话对嘛。所以还是想简单点。如果V0不是fair value的话，这一题他就会让你求V0是多少了，CFA一道小题不会让你进行多重计算的。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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WallE_品职答疑助手 · 2021年07月22日

嗨，爱思考的PZer你好：

这V0是表一中给的，是已知信息，您没必要去怀疑已知信息。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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xxxxsdadas · 2021年07月22日

？？我不是怀疑，它只是写了price，并没有说这就是合理定价，而且后面又说这个bond的OAS是多少多少，很容易让思路转向是不是要求它的合理定价那个方向。所以我才来提问看看哪里能看出已知条件就是V0

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