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蜗牛也是牛Megan · 2024年05月30日

这道题的DF是怎么计算出来的？

  1. CFA II
  2. Fixed Income

NO.PZ2019011002000001

问题如下：

Tim is a member of credit research team in a wealth management firm. The team is analyzing a set of bonds with some similar characteristics.

Bond A is a zero-coupon 5-year corporate bond with a par value of $1000. Tim believes that the risk-neutral probability of default (Hazard rate) for each date for the bond is 1.50%, and the recovery rate is 25%. Assume there is no interest rate volatility and the government bond yield curve is flat at 2%.

The market price of the bond A is $850, according to the information above the bond is:

选项：

A.

fairly value

B.

overvalued

C.

undervalued

解释：

C is correct

考点：考察对Credit risk计量，从而计算Fair value。

解析：

本题要按照常规步骤计算债券的Value。

第一步：用无风险利率进行折现，计算债券在每个时间点的价值。本题假设无风险利率没有波动为2%

经过计算Exposure为下图所示。

第二步：计算Recovery；Recovery = exposure × recovery rate，已知本题的Recovery rate为25%，可计算Recovery为下图所示。

第三步：计算Loss given default；

LGD=Exposure – recovery

第四步：计算Probability of default (POD)；由题干已知the risk-neutral probability of default (Hazard rate) for each date for the bond is 1.50%；则第一期的POD为1.5%，随后每一期的POD，等于Hazard rate乘以上一期存活的概率即上一期POS。因此需要知道每一期的POS；每一期POS可知：

(100%-1.5%)1=98.5%

(100%-1.5%)2=97.0225%

(100%-1.5%)3=95.5672%

(100%-1.5%)4=94.1337%

(100%-1.5%)5=92.7217%

第六步：计算Expected loss；有Expected loss = LGD × POD

第七步：计算每一期的折现率，本题假设利率是恒定的2%；

第八步：计算Expected loss的现值，PV expected loss

通过用无风险利率折现该Bond得到的现值为：905.7308

则债券的合理价值为：905.7308 – 49.44 = 856.29

因此当前债券是相对被低估的。

所以每一年用无风险利率算出来的吗

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1 个答案

吴昊_品职助教 · 2024年05月30日

嗨，努力学习的PZer你好：


是的。discount factor是每一期折现率的倒数。

比如：DF1 = 1/1.02 = 0.9804

DF2 = 1/(1.02^2) =0.9612

DF3 = 1/(1.02^3) = 0.9423

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2024-04-05 14:11 1 · 回答

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2023-11-09 21:59 1 · 回答

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2023-10-12 20:23 1 · 回答

NO.PZ2019011002000001 这样做的答案是一样的 请教老师CVA类型的题目什么时候能这样做 什么时候不能呢？

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