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豌豆妤22 · 2021年02月17日

问一道题：NO.PZ201812310200000101 第1小题 [ CFA II ]

  1. CFA II
  2. Fixed Income

* 问题详情，请 查看题干

问题如下：

The market price of bond B1 is€875. The bond is:

选项：

A.

fairly valued.

B.

overvalued.

C.

undervalued.

解释：

B is correct.

The following table shows that the credit valuation adjustment (CVA) for the bond is

€36.49, the sum of the present values of expected loss. The steps taken to complete the table are as follows.

Step 1: Exposure at Date T is 1000 (1+r) 4−T , where r is 3%. That is, exposure is computed by discounting the face value of the bond using the risk-free rate and the number of years until maturity.

Step 2: Recovery = Exposure × Recovery rate

Step 3: Loss given default (LGD) = Exposure – Recovery

Step 4: Probability of default (POD) on Date 1 is 1.50%, the assumed hazard rate. The probability of survival (POS) on Date 1 is 98.50%.

For subsequent dates, POD is calculated as the hazard rate multiplied by the previous date’s POS.

For example, to determine the Date 2 POD (1.4775%), the hazard rate of (1.50%) is multiplied by the Date 1 POS (98.50%).

Step 5: POS in Dates 2–4 = POS in the previous year – POD

(That is, POS in Year T= POS in year [ T– 1] – POD in Year T.)

POS can also be determined by subtracting the hazard rate from 100% and raising it to the power of the number of years:

(100% – 1.5000%)1 = 98.5000%

(100% – 1.5000%)2 = 97.0225%

(100% – 1.5000%)3 = 95.5672%

(100% – 1.5000%)4 = 94.1337%

Step 6: Expected loss = LGD × POD

Step 7: Discount factor (DF) for Date T is 1 (1+r) T , where r is 3%.

Step 8: PV of expected loss = Expected loss × DF

Value of the bond if the bond were default free would be 1,000 × DF for Date 4 = €888.49.

Fair value of the bond considering CVA = €888.49 – CVA = €888.49 – €36.49 = €852.00.

Because the market price of the bond (€875) is greater than the fair value of €852, B is correct.

A is incorrect because the market price of the bond differs from its fair value. C is incorrect because although the bond’s value if the bond were default free is greater than the market price, the bond has a risk of default, and CVA lowers its fair value to below the market price.

老师，讲解我看懂了，就是有类疑问就是对于这样的题目中，没有明确是 flat curve的假设下，我可能会把第一个假设当作干扰项pass掉，直接用后面二叉树来求fair value，那么如何辨别这样的情况呢？

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1 个答案

WallE_品职答疑助手 · 2021年02月19日

同学您好，

一般考试的时候呀，咱们针对一小题必然不会太复杂，这一题的计算量已经很大了，如果在让咱们用二叉树来求必定时间要花很多。

当考试的时候，用二叉树和这种求CVA或者fair value的题目会分开的很明显的，可能在做课后题或者往年的mock的时候会有这种担心，那都是因为老题目了或者有些出的不够严谨。不过考试时完全不用担心分辨不出来，考试的时候基本就是1-2段对应一道题目，后面的题目与前面没有关系。

如果之后碰见了疑似辨别不清楚的题目，你可以具体的列出来然后我们在来探讨。

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