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dazttle · 2024年07月02日

用畫圖的方法解釋嗎?

NO.PZ2023040701000073

问题如下:

Hsu then selects the four bonds issued by RW, Inc. given in Exhibit 2. These bonds all have a maturity of three years and the same credit rating. Bonds #4 and #5 are identical to Bond #3, an option-free bond, except that they each include an embedded option.

In Exhibit 2, the bond whose effective duration will lengthen if interest rates rise is:

选项:

A.

Bond #3

B.

Bond #4

C.

Bond #5

解释:

Correct Answer: B

Effective duration indicates the sensitivity of a bond’s price to a 100 bps parallel shift of the benchmark yield curve assuming no change in the bond’s credit spread. The effective duration of an option-free bond such as Bond #3 changes very little in response to interest rate movements. As interest rates rise, a call option moves out of the money, which increases the value of the callable bond and lengthens its effective duration. In contrast, as interest rates rise, a put option moves into the money, which limits the price depreciation of the putable bond and shortens its effective duration. Thus, the bond whose effective duration will lengthen if interest rates rise is the callable bond, i.e., Bond #4.

麻煩老師可以畫圖解釋嗎?謝謝

1 个答案

pzqa31 · 2024年07月03日

嗨,努力学习的PZer你好:


这道题更简单的方法是通过定性理解判断的。


callable bond与Putable bond 的ED小于option free bond 的ED,原因是这两种债有可能会提前行权结束,所以剩余到期日短,ED就小。


对于callable 来说,利率下降,发行人才有可能提前行权买回,所以,利率下降,callable bond的effective duration更小了。


对于putable 来说,利率上涨,投资人才有可能提前行权卖回,所以,利率上涨,putable bond的ED更小了。


本题问的是,如果利率上涨,哪种债的ED可能变大,

先排除option free bond,它的ED与利率涨跌关系不大

callable 是利率下跌ED变小,那么如果利率上涨,发行人不会行权,callable bond就变成了option free bond,也就是ED变大了。

putable 是利率上涨ED变小,那么如果利率下跌,投资人不会行权,putable bond就变成了option free bond,也就是ED变大了。

所以,如果利率上涨,只有callable 的ED会变大。


然后贴一下callable bond和putable bond的图形给你参考,可以看到callable bond在利率下降的时候,duration(斜率)是逐渐减小的。而对于putable bond,在利率上涨的时候,duration会更小。

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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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