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Pina · 2020年06月19日

问一道题：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：

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

老师好，这题原来是指，在第一年和第二年里有call option. 一开始读题，以为是说， callable 从一年后开始，维持两年。如果题目要表达forward callable bond, 一般会怎么表达？比如，三年bond, 第一年和第二年没有callable, 从第三年开始才有call option for the issuer 的话，英语是怎么表达？谢谢。

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吴昊_品职助教 · 2020年06月19日

这就是我前面和你说过的call schedule，这道题中callable at par in one year and two years from today，意思就是在第一年末，第二年末可以以面值赎回。如果callable bond直到第三年末才能被赎回，那么就是callable at XX price in three years from today。

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