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必过1030_ · 2022年05月24日

选项b的正确说法是什么?

NO.PZ2021120102000015

问题如下:

Which of the followingstatements about credit spread measures is most accurate?

选项:

A.

The DM is the yield spread over the MRR established upon issuanceto compensate investors for assuming an issuer’s credit risk.

B.

The Z-DM will be above the DM if the MRR is expected to remain constant over time.

C.

The yield spread for a corporate bond will be equal to the G-spread if the government benchmark yield curve is flat.

解释:

Cis correct.

Theyield spread is the simple difference between a bond’s all-in YTM and a current on-the-run governmentbond of similar maturity, while the G-spread isan interpolation of government benchmark yields. If the government bond yieldcurve is flat, these two measures will equal one another.

选项b的正确说法是什么?

1 个答案

pzqa015 · 2022年05月26日

嗨,努力学习的PZer你好:


如果MRR remain constant,那么Z-DM=DM

如果MRR曲线向上倾斜(隐含着未来的MRR大于现在的MRR),则Z-DM小于DM。原因如下

一方面,不论是用Z-DM折现求和,还是DM折现求和,得到的债券现在的价格是相等的,也就是说两张图片中的PV是一样的。另一方面,在任何一个求价格的公式中,对PV影响最大的一期现金流是最后一期,也就是要考虑FV的一期现金流。

 

那么我们可以进步简化为让上面两个公式的最后一项相等,也就是

(((MRR+QM)*FV)/m+FV)/(1+(MRR+DM)/m)^N=(((zN+QM)*FV)/m+FV)/(1+(zn+ZDM)/m)^N

如果预期future MRR上升,也就是zN>MRR。

单看分子:(zN+QM)*FV>(MRR+QM)*FV

看分母:(1+(zn+ZDM)/m)^N也应该大于(1+(MRR+DM)/m)^N,

但由于分母有N次幂,所以,(zn+ZDM)/m并不会比(MRR+DM)/m大太多(N次幂放大后,(1+(zn+ZDM)/m)^N才比(1+(MRR+DM)/m)^N大),可以认为二者是接近相等的,那么既然二者相等,由于zn>MRR,ZDM一定是小于DM的。

 


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