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追风少年NKU · 2021年08月29日

这题出的有点让人摸不清头脑

  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%

这题出的有点让人摸不清头脑

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1 个答案

李坏_品职助教 · 2021年08月30日

嗨，努力学习的PZer你好：


这道题考察的是risk-neutral风险中性违约概率和real-world实际情况下的违约率之间的关系。


根据notes的这部分的考点：

Risk-neutral default probabilities are calculated from market information, while real-world default probabilities are based on historical data. Typically, real-world default probabilities are less than risk-neutral default probabilities.

这里可以看出risk-neutral违约概率=real-world违约率+default risk Premium + liquidity premium。

treasury bond是几乎没有违约概率的，所以这道题里的计算与它无关。


直接看bond A：面值100，Price是95，说明市场对它的总的违约损失预期（risk-neutral default probability）是5%。这个5%包括了实际情况的违约概率、投资者要求的违约风险补偿（default risk premium）以及流动性补偿（liquidity premium）三个部分。

设real-world违约率是x, 那么5% = x + 1% + 2% , x = 2%。

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