问题如下:
Tim, a credit analyst, is valuing bond B. Bond B is a 5-year corporate bond with a par value of $1000. The bond has a fixed annual coupon rate of 6%, and the coupon is paid annually.
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%.
According to the information above, the fair value of bond B is closet to:
选项:
A.1083.29
B.1129.86
C.1231.29
解释:
B is correct.
考点:考察对Credit risk计量,从而计算Fair value。
解析:
本题按照步骤计算债券价值即可,与上一题的区别是本题的债券每期有Coupon。
第一步:计算每一期的Exposure;第五期的Exposure为1060;
第四期的Exposure,为债券第五年现金流在第四期的现值,加上第四期的Coupon;
即:
第三期的Exposure,为债券第四年,第五年现金流在第三期的现值,加上第三期的Coupon;
即:
依次类推可以计算出每一期的Exposure;计算CVA的步骤和上题一致;有表格:
用2%的无风险利率对该债券进行折现,得到的现值为:1188.538
则可以得到债券的Fair value为:1188.538 - 58.6754 = 1129.86
发现一个问题 ,这个求第二年以及之后的EL时,第二年的EL 是不是应该直接把敞口乘以违约概率1.5%和第一年的存活概率98.5%而不需要乘以98.5%的平方,再求第三年的也是前两年存活的概率98.5%的平方乘以1.5%而不是用98.5%的三次方作为存活概率呢?