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台风来了 · 2023年08月13日

关于收益率曲线的倾斜和含权债券的call option的价值

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NO.PZ202304070100007402

问题如下:

All else being equal, if the shape of the yield curve changes from upward sloping to flattening, the value of the option embedded in Bond #2 will most likely:

选项:

A.

decrease.

B.

remain unchanged.

C.

increase.

解释:

Correct Answer: C

Bond #2 is a callable bond, and the value of the embedded call option increases as the yield curve flattens. When the yield curve is upward sloping, the one-period forward rates on the interest rate tree are high and opportunities for the issuer to call the bond are fewer. When the yield curve flattens or inverts, many nodes on the tree have lower forward rates, which increases the opportunities to call and, thus, the value of the embedded call option.

老师,您好!


收益率曲线当前向上倾斜,但预期将变得平坦。前者表明一期forward rate相对spot rate较高,后者预期forward rate相对spot rate较低。我理解这只是单纯从收益率曲线的形状做一个大概的定性判断。但是变得平坦,既可以是短期利率相对上升,也可以是长期利率相对下降。如果是短期利率相对上升,那么债券价格下跌,call的价值也就会下降了。


麻烦老师再解释一下吧,谢谢!

1 个答案

pzqa015 · 2023年08月14日

嗨,爱思考的PZer你好:



根据Pure expectation theory,长期利率可以看成现在短期利率和未来短期利率的平均值

那么如果曲线变平,意味着长短期利率的spread下降,也就是未来短期利率下降,所以,callable更容易行权,她的embedded option value会上涨。

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