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YAO Monica · 2022年02月02日

OAS理解

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：

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

第一步：根据OAS上调利率

第二步：再计算ED（增/减30bps）

如何理解第一步？

个人理解：OAS表示含权债券的利率。所以图中直接给的利率是不含权利率，需要先考虑OAS再计算含权债券的ED是吗？

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pzqa015 · 2022年02月02日

嗨，爱思考的PZer你好：

OAS是剔除权利影响后的spread，用来反映含权债相对于benchmark的spread。

题目说了表2的A和B分别表示benchmark yield向上或向下移动30bp，所以，需要加上OAS后来计算债券价格。

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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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