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Summer. · 2021年10月05日

读不懂题

NO.PZ2020021204000016

问题如下:

The six-month, 12-month, 18-month, and 24-month zero rates are 5%, 5.5%, 6%, and 6.5% (all measured with semi-annual compounding) respectively. What is the two-year par yield for a bond paying coupons every six months?

选项:

解释:

The par yield is the coupon rate c satisfying

c/21+0.05/2+c/2(1+0.055/2)2+c/2(1+0.06/2)3+100+c/2(1+0.065/2)4=100\frac{c/2}{1+0.05/2}+\frac{c/2}{{(1+0.055/2)}^2}+\frac{c/2}{{(1+0.06/2)}^3}+\frac{100+c/2}{{(1+0.065/2)}^4}=100

It is 6.46%. Alternatively, we can use Equation (cm)A  +  100d  =  100\left(\frac cm\right)A\;+\;100d\;=\;100. In

this case m= 2, d= 0.8799, and A= 3.7179.

这道题是说一个2年的债券,每6,12,18,24个月的zero rate 不同吗?完全读不懂题,能不能吧题干拆解一下,讲解一下呢。谢谢

1 个答案

品职答疑小助手雍 · 2021年10月05日

同学你好,给的条件是抛开债券来说,市场上的利率。题面的意思是市场上6,12,18,24个月的zero rate分别是这么几个。

要算的是一个半年付息的两年期债券的par yield,也就是说这题其实考的是rate之间的转换。

转换方法按照基础班讲义par yield那一节(大约258页左右)直接套公式就好了。


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