开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

Olinaaaaa · 2024年04月14日

还是不太懂year 5的算法

NO.PZ2023090401000005

问题如下:

Question A credit risk analyst at a wholesale bank is estimating annual default probabilities of a 5-year loan that has just been extended to a corporate borrower. The analyst determines from rating agency data that the 5-year cumulative default probability of bonds from this borrower with identical terms and seniority is 6.2%, and uses this information to calculate the 5-year survival rate for the borrower. If the borrower’s average hazard rate for the first 4 years of the loan is 1.1%, what is the unconditional default probability of the borrower during year 5 of the loan?

选项:

A.

1.71%

B.

1.80%

C.

1.90%

D.

1.98%

解释:

Explanation:

C is correct. The unconditional default probability between the end of year 4 and the end of year 5 is calculated as

exp(-̅ 4 4) exp(-̅ 5 5)

where ̅4 and ̅5 are the average hazard rates between today and end-of-year 4 and end-of-year 5, respectively. The term

exp(-̅5 5)

in the equation above represents the probability of survival (or survival rate) to the end of year 5. This is equal to one minus the cumulative default probability to the end of year 5, given as 6.2%. Therefore, the 5-year survival rate is

1 − 0.062 = 0.938

and the unconditional default probability during the fifth year of the loan is

exp(−0.011 4) 0.938 = 0.956954 0.93800 = 0.01895 or 1.895%

A is incorrect. This incorrectly calculates the survival rate as exp(−0.062) = 0.939883, and uses this to calculate the unconditional default probability = 0.956954 – 0.939883 = 0.017071 = 1.71%.

B is incorrect. This incorrectly calculates the unconditional default probability as 0.062 − 4 0.011.

D is incorrect. This is the conditional default probability during the fifth year, or 0.01895/exp(0.011 4).

Section: Valuation and Risk Models

Learning Objective: Define and use the hazard rate to calculate the unconditional default probability of a credit asset

Reference: Global Association of Risk Professionals. Valuation and Risk Models. New York, NY: Pearson, 2022. Chapter 4. External and Internal Credit Ratings

我懂during5就是求year4 and 5之间的违约概率 但是不太懂year 5为什么不能直接用那个公式 而是求出survival rate

1 个答案

李坏_品职助教 · 2024年04月14日

嗨,从没放弃的小努力你好:


本题最后问的是在第五年之内违约的概率是多少,一个贷款幸存到第四年之后,剩下就是两种情况:1. 在第五年内违约,2.幸存到第五年年末。

所以可以用幸存到第四年的概率exp(-h4 * 4)减去幸存到第五年年末的概率exp(-h5 * 5),也就得出情况1的概率。


题目只是告诉我们h4是1.1%,h5没有告诉我们,所以无法直接用公式求出exp(-h5 * 5)。

不过,幸存到第五年年末的概率exp(-h5 * 5) = 1-第五年的累计违约概率 = 1-6.2% = 0.938,这样就不需要h5了。


最后用exp(-h4 * 4) - 0.938= 0.01895 得出在第五年内违约的概率。

----------------------------------------------
努力的时光都是限量版,加油!

  • 1

    回答
  • 0

    关注
  • 359

    浏览
相关问题

NO.PZ2023090401000005 问题如下 Question A cret risk analyst a wholesale bank is estimating annufault probabilities of a 5-yelothhjust been extento a corporate borrower. The analyst termines from rating agenta ththe 5-yecumulative fault probability of bon from this borrower with inticterms anseniority is 6.2%, anuses this information to calculate the 5-yesurvivrate for the borrower. If the borrower’s average hazarrate for the first 4 years of the lois 1.1%, whis the uncontionfault probability of the borrower ring ye5 of the loan? A.1.71% B.1.80% C.1.90% 1.98% Explanation: C is correct. The uncontionfault probability between the enof ye4 anthe enof ye5 is calculateasexp(-ℎ̅ 4 ∗ 4) − exp(-ℎ̅ 5 ∗ 5)where ℎ̅4 anℎ̅5 are the average hazarrates between toy anenof-ye4 anenof-ye5, respectively. The termexp(-ℎ̅5 ∗ 5)in the equation above represents the probability of surviv(or survivrate) to the enof ye5. This is equto one minus the cumulative fault probability to the enof ye5, given 6.2%. Therefore, the 5-yesurvivrate is 1 − 0.062 = 0.938 anthe uncontionfault probability ring the fifth yeof the lois exp(−0.011 ∗ 4) − 0.938 = 0.956954 − 0.93800 = 0.01895 or 1.895% A is incorrect. This incorrectly calculates the survivrate exp(−0.062) = 0.939883, anuses this to calculate the uncontionfault probability = 0.956954 – 0.939883 = 0.017071 = 1.71%. B is incorrect. This incorrectly calculates the uncontionfault probability 0.062 − 4 ∗ 0.011. is incorrect. This is the contionfault probability ring the fifth year, or 0.01895/exp(0.011 ∗ 4). Section: Valuation anRisk Mols Learning Objective: fine anuse the hazarrate to calculate the uncontionfault probability of a cret assetReference: GlobAssociation of Risk Professionals. Valuation anRisk Mols. New York, NY: Pearson, 2022. Chapter 4. ExternanInternCret Ratings 原解题步骤中有乱码,无法清晰的看到如何计算

2024-04-10 20:52 1 · 回答