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Aaaashley · 2023年03月30日

关于利率去年化之后时间的转化

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.

为什么折现的时间没有按照真实的0.5,1,1.5,2而是按照1,2,3,4呢?

1 个答案

品职答疑小助手雍 · 2023年03月30日

同学你好,semi-annual compounding的折现方式通常是利率除以2,然后按期(1,2,3,4)折。

而不是用原始的年化利率按时间(0.5,1,1.5,2)折

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