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yingya0706 · 2024年10月12日

折价发行债券的duration

NO.PZ2023052301000021

问题如下:

Exceptions to the maturity effect exist for bonds that have:

选项:

A.

long maturities, make small coupon payments, and trade at a discount.

B.

short maturities, have high coupon rates, and trade at a discount.

C.

long maturities, have high coupon rates, and trade at a premium.

解释:

A is correct. Exceptions to the maturity effect are rare and occur only for low-coupon (but not zero-coupon) long-term bonds trading at a discount.

B is incorrect because the maturity effect holds for bonds that have short maturities and high coupons.

C is incorrect because the maturity effect always holds on bonds priced at a premium above par value.

老师在前面别的同学提问的解答中明白了那个图,但是为什么discount发行的债券duration的图会先增加后下降呢

1 个答案

笛子_品职助教 · 2024年10月12日

嗨,努力学习的PZer你好:


老师在前面别的同学提问的解答中明白了那个图,但是为什么discount发行的债券duration的图会先增加后下降呢

Hello,亲爱的同学~

这里需要引入一个知识点:永续债券(perpetuity)。

永续债券,是指没有到期日的债券,那么它的久期,是不是无限大,并不是的。它的久期是一个常数:(1+r)/r。

正常来说,一个债券,它的到期日越长,久期也越大。但是当到期日大到一定程度后,它就成了一个类似永续债的债券,于是,久期向永续债的久期回归。


所以先增加的原因,是因为人们把它当作了一个正常债券,用的是正常债券的规律:到期越长,久期越大。

之后减少的原因,是因为人们发现它其实是个永续债,因此回归了永续债的久期。


这个临界点老师理解,可能是和人的寿命有关。

例如,一个10年期的债券,人们会认为10年是可以等到的。一个30年的债券,人们觉得时间有点久,但也是可以等到的,从青年等到老年。

但一个50年的债券,100年的债券,可能人们认为这个时间太长了,等不到了,于是就把它当成一个永续债,用永续债的方法算久期。

这就导致折扣债的久期先上升,后下降。

----------------------------------------------
就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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