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pinzhixiaoguo · 2022年11月11日

想问一下这道题不需要正式计算YTM吗？

  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%

债券的par value是100，当前市价95，coupon是2.5，假设1年后到期的话，102.5/（1+YTM）=95，则YTM=7.89%。

（YTM-Rf）/（1+YTM）=π*（1-f），到这里就卡住了，不知道LGD需要的f，后续进行不下去了？

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李坏_品职助教 · 2022年11月11日

嗨，努力学习的PZer你好：


虽然YTM的算法是比较精确的，但是因为条件不足，没有告诉关于LGD的信息，所以就不能用YTM这个算法了。


这道题用的是Notes里面给的算法：市场给出的定价是95，债券面值100，说明该债券风险中性违约概率是5%。这个风险中性违约概率包含了：流动性风险溢价、违约风险溢价和实际的违约风险。




或者这么理解：这个债券总的风险溢价（流动性风险+违约风险）是2% +1% = 3%，理论上应该值97块钱（3%的折价）。但是市场定价只有95块钱，投资人只愿意付95块钱。这少的2块钱（2%），就是现实世界中的违约概率了。

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努力的时光都是限量版，加油！

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