NO.PZ2019011002000001
问题如下：
Tim is a member of credit research team in a wealth management firm. The team is analyzing a set of bonds with some similar characteristics.
Bond A is a zero-coupon 5-year corporate bond with a par value of $1000. Tim believes that the risk-neutral probability of default (Hazard rate) for each date for the bond is 1.50%, and the recovery rate is 25%. Assume there is no interest rate volatility and the government bond yield curve is flat at 2%.
The market price of the bond A is $850, according to the information above the bond is:
选项：
A.fairly value
B.overvalued
C.undervalued
解释：
C is correct
考点：考察对Credit risk计量，从而计算Fair value。
解析：
本题要按照常规步骤计算债券的Value。
第一步：用无风险利率进行折现，计算债券在每个时间点的价值。本题假设无风险利率没有波动为2%
经过计算Exposure为下图所示。
第二步：计算Recovery；Recovery = exposure × recovery rate，已知本题的Recovery rate为25%，可计算Recovery为下图所示。
第三步：计算Loss given default；
LGD=Exposure – recovery
第四步：计算Probability of default (POD)；由题干已知the risk-neutral probability of default (Hazard rate) for each date for the bond is 1.50%；则第一期的POD为1.5%，随后每一期的POD，等于Hazard rate乘以上一期存活的概率即上一期POS。因此需要知道每一期的POS；每一期POS可知：
(100%-1.5%)1=98.5%
(100%-1.5%)2=97.0225%
(100%-1.5%)3=95.5672%
(100%-1.5%)4=94.1337%
(100%-1.5%)5=92.7217%
第六步：计算Expected loss；有Expected loss = LGD × POD
第七步：计算每一期的折现率，本题假设利率是恒定的2%；
第八步：计算Expected loss的现值，PV expected loss
通过用无风险利率折现该Bond得到的现值为：905.7308
则债券的合理价值为：905.7308 – 49.44 = 856.29
因此当前债券是相对被低估的。
为何EL随时间呈递增而递增？越早违约不是应该损失越多吗？
