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小太阳 · 2023年11月23日

两个半年的违约率

NO.PZ2023101601000022

问题如下:

Suppose XYZ Corp. has two bonds paying semiannually according to the following table. The recovery rate for each in the event of default is 50%. For simplicity, assume that each bond will default only at the end of a coupon period. The market-implied risk-neutral probability of default for XYZ Corp. is

选项:

A.

Greater in the first six-month period than in the second

B.

Equal between the two coupon periods

C.

Greater in the second six-month period than in the first

D.

Cannot be determined from the information provided

解释:

First, we compute the current yield on the six-month bond, which is selling at a discount. We solve for y such that 99 = 104/(1 + y/2) and find y = 10.10%. Thus, the yield spread for the first bond is 10.1 − 5.5 = 4.6%. The second bond is at par, so the yield is y= 9%. The spread for the second bond is 9 − 6 = 3%. The default rate for the first period must be greater. The recovery rate is the same for the two periods, so it does not matter for this problem.

老师您好,请问这是哪个知识点里面的内容呀?可以解释一下这道题嘛?谢谢老师

1 个答案

DD仔_品职助教 · 2023年11月24日

嗨,从没放弃的小努力你好:


考察信用风险里的spead与违约概率之间的关系

根据答案提供的计算公式:算出来的第一个bond的spread4.6%是前六个月的,后面bond一年的spread是3%(一年的平均情况)。

题目又说recovery 前后一样。那显然就是前六个月的PD高,后六个月PD低了。

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