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。
題目不是說zero coupon rate嗎 那不是應該只有一筆現金流嗎