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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， ” callable at par in one year and two years from today" 可不可以理解为callable at par 在一年后和两年后有？也就是第2 年和第3 年才有callable at par on this bond? 下面数轴画的对吗？利率上面标的year 0, year 1 and year 2 是时点的概念是吗?

我下面相对应的数轴（表时间段）画得对吗？

用year 1 的利率去折第2 年的CF,用year 2 的利率去折year 3 's CF. 是吗？谢谢。

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吴昊_品职助教 · 2020年06月19日

题目的意思是在第一年末和第二年末可以以面值赎回。也就是说在year1和year2两个时间点我们需要将折现得到的价格和strike price进行比较。

你画的时间轴是对的。第三年末的现金流用year2的利率进行折现，第二年末的现金流用year1的利率进行折现，以此类推。

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