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dazttle · 2024年07月02日

用公式 Vcallable = Vstraight - Vcall 解釋

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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.

用公式 Vcallable = Vstraight - Vcall

利率下降,price increase,更容易行權,Vcall 不是會上升嗎?接著Vcallable會下降?

1 个答案

吴昊_品职助教 · 2024年07月03日

嗨,努力学习的PZer你好:


1、当利率下降的时候,正常不含权债券,债券价格自然上升(绿色线)。但是callable bond在利率下降的时候,有一个价格上限,这个上限是call price。一旦触及到上限,价格就涨不上去了(红色线)。

也就是说,只要利率下降,所有债券价格都是上升的,只不过callable bond的价格涨幅较小。红色线涨幅比绿色线涨幅小。

2、Vcall的价格,就要看行权的可能性是增加还是减小。利率下降的时候,call option的行权可能性增大,所以Vcall上升。

3、你所列的公式,只是想通过不含权债券和含权债券的价格差,反求一下内含的option价格。并不能简单用来判断各个部分的上涨和下跌。

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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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