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滴滴姐姐~ · 2021年10月11日

来问问这题。。。

  1. FRM II
  2. Credit Risk Measurement And Management

NO.PZ2020033003000067

问题如下：

Jane is asked to calculate the risk-neutral and real-world default probabilities of the bond A. She collected the following datas. The market price of the bond A with a face value of 100 is 95. The liquidity premium and credit risk premium are 2% and 1% respectively. The coupon rate of newly issued treasury bond is 2.5%. The expected inflation is 0.8%.

选项：

Risk-neutral probability
Real-world probability
A.
Risk-neutral probability 2%
Real-world probability 5%
B.
Risk-neutral probability 5%
Real-world probability 2%
C.
Risk-neutral probability 5%
Real-world probability 4.2%
D.
Risk-neutral probability 4.2%
Real-world probability 5%

解释：

B is correct.

考点：Infer Credit Risk from Corporate Bond Prices

解析：risk-neutral default probability 100-95=5%

risk-neutral probability = real-world probability + credit risk premium + liquidity premium

real-world probability = 5% - 2%-1% = 2%

  1. 是不是少条件呀，我只能通过real world < calculated 安排出来BC 然后LGD没说是多少呀（看之前的解析 我就假设LGD = 100%吧）
  2. 看了 李坏_品职助教 的解答，有这么几个问题
  • Figure29.1 不懂为什么有了一个default risk 还有一个default risk premium，就像这道题一样 要我们求default probability，但还告诉我们一个credit premium？【我其实就是不太懂 risk-neutral违约概率=real-world违约率+default risk Premium + liquidity premium这个公式？好像老师上课没讲呀 这里提到的notes又是哪本书嘞？】
  • 为啥这道题不考虑treasury呢？我的点在于：
  • 看见expected inflation我感觉要走补偿的那个路子 就 rf+通胀补偿+liquidity补偿+credit补偿 = YTM 然后这个就可以和那个简化的式子结合起来了 就是苦于没有LGD而已。。。


希望我问的可以understandable hhh（蟹蟹蟹蟹~）

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1 个答案

李坏_品职助教 · 2021年10月12日

嗨，从没放弃的小努力你好：


notes就是Kaplan出版的FRM notes，是国外比较权威的一个辅导机构出版的教材。


treasury bond是美国的国库券，国债的一类，可以认为是没有credit risk的，所以不考虑。


按照Notes里面的逻辑，市场给出的定价是95，这个定价是根据risk neutral 算出来的，就说明real world违约概率、投资者要求的default risk premium再加上流动性补偿（liquidity premium）三个部分加起来是5%，这样real world default probability是2%。


至于你说的inflation在这个题目里是不考虑的，corporate bond的risk neutral 违约率不考虑通货膨胀的问题，除非是跟通胀挂钩的债券才会考虑

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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