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亚利 · 2023年06月23日

关于0到5年用算数评均

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2020011303000101

问题如下：

If the hazard rate is 1.5% per year for the first three years and 2.5% per year for the next three years, what is the probability of default during the first two years? What is the average hazard rate for the first five years? What is the probability of default between years two and five?

解释：

The probability of default during the first two years is 1-exp(−0.015 × 2) = 0.02955. The average hazardrate during the first five years is (1.5 × 3 + 2.5 × 2)/5 = 1.9%. The probability of default during the first five years is 1-exp(−0.019 × 5) = 0.09063. The probability of default between years two and five is 0.09063 − 0.02955 = 0.06107.

题目问：如果前三年的hazard rate为每年 1.5%，后三年为每年 2.5%，那么前两年的违约概率是多少？前五年的平均hazard rate是多少？第二年和第五年之间违约的概率是多少？

PD(0-2)=1-e^(-h*t)=1-e^(-1.5%*2)=0.02955

平均h for 0-5 year=(1.5%*3+2.5%*2)/5=1.9%

PD(0-5)=1-e^(-1.9%*5)=0.09063

PD(2-5)=PD(0-5) - PD(0-2)=0.09063-0.02955=0.06107


如果0-5年可以用算数平均算h，那最后一问为什么不用2-5年算数平均h来计算违约概率呢？

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1 个答案

品职答疑小助手雍 · 2023年06月24日

同学你好，可以算，但是要注意计算逻辑。

你用算数平均h算出来的是conditional 的pd（结果是0.062933），unconditional的PD的话要再乘以前两年的存活概率1-0.02955

这样就跟答案一致了。

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NO.PZ2020011303000101 问题如下 If the hazarrate is 1.5% per yefor the first three years an2.5% per yefor the next three years, whis the probability of fault ring the first two years? Whis the average hazarrate for the first five years? Whis the probability of fault between years two anfive? The probability of fault ring the first two years is 1-exp(−0.015 × 2) = 0.02955. The average hazarate ring the first five years is (1.5 × 3 + 2.5 × 2)/5 = 1.9%. The probability of fault ring the first five years is 1-exp(−0.019 × 5) = 0.09063. The probability of fault between years two anfive is 0.09063 − 0.02955 = 0.06107. 题目问如果前三年的hazarrate为每年 1.5%，后三年为每年 2.5%，那么前两年的违约概率是多少？前五年的平均hazarrate是多少？第二年和第五年之间违约的概率是多少？P0-2)=1-e^(-h*t)=1-e^(-1.5%*2)=0.02955平均h for 0-5 year=(1.5%*3+2.5%*2)/5=1.9%P0-5)=1-e^(-1.9%*5)=0.09063P2-5)=P0-5) - P0-2)=0.09063-0.02955=0.06107 老师您好，我计算b问题的时候直接这么算的1 - （e^ -0.015*3)*(e^ -0.025*2) = 0.090627这样是不是也可以的？

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