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老虎爱小猪™ · 2021年04月06日

panel B里利率为什么不考虑callable的影响呢，第一年年末不是应该被赎回了吗？

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：

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

为什么panel B里利率为4.9377%时没有考虑call option的影响呢，小于5.25%，所以issuer第一年年末应该是会赎回的啊

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WallE_品职答疑助手 · 2021年04月06日

嗨，从没放弃的小努力你好：

这里表格1说是callable at par也就是按价格100来赎回，并不是callable at interest rate. 所以从T2 往T1折现，要看他的价值是否超过了100，没有超过100就不会被执行。

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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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