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lin · 2020年10月25日

问一道题：NO.PZ2016082406000034

  1. FRM II
  2. Credit Risk Measurement And Management

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：

ANSWER: A

First, we compute the current yield on the six-month bond, which is selling at a discount. We solve for y* such that 99=1041+y∗20099\text{=}\frac{104}{1+\frac{y\ast}{200}} and find y∗=10.10%y\ast\text{=}10.10\%. Thus the yield spread for the first bond is 10.1-5.5=4.6%10.1\text{-}5.5\text{=}4.6\%. The second bond is at par, so the yield is y∗=9%y\ast\text{=}9\%. The spread for the second bond is   9-6=3%\;9\text{-}6\text{=}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.

老师好，这道题我感觉不用考虑那么复杂，感觉都没有考YTM-Rf≈PD*(1-RR)这个知识点。题目问题问的是XYZ这家公司的违约概率是在上半年高还是下半年高。XYZ公司一共包含了两个债券，第一个A债券只有半年，在第6个月付一次息，第二个B债券是一年，分别在第6个月和1年末付息；而题目还提到了在付息的时候可能会发生违约，那么其实在第6个月的时候，XYZ这家公司违约的概率就是A违约B不违约+B违约A不违约+AB都违约，而在1年末的违约概率是B违约，这样一比较，肯定是在第6个月的时候要更高吧？之前有个同学这么理解的，我觉得很在理，想问问老师这么理解是不是正确的

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1 个答案

品职答疑小助手雍 · 2020年10月26日

嗨，从没放弃的小努力你好：


我觉得这样想就失去考题的意义了。考察角度肯定还是从RR一样的话，spread的对比入手来的。

不过这个老题出的确实不好，不用太在意这个题啦。


-------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！


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