NO.PZ2020033002000024
问题如下：
ABC currently has an A credit rating and has issued two-year zero-coupon bonds, and the market expects the company to maintain its rating at A, downgrade to BBB, or upgrade to AA in one year's time with probabilities of 85%, 10%, and 5%, respectively. Assuming a flat risk-free yield curve with a value of 1% and credit spreads of 70, 100 and 300 basis points at the AA, A and BBB levels, respectively, all interest rates are compounded annually. What is the expected value of a zero-coupon bond after one year?
选项：
A.96.15 B.98.04
C.98.33
D.97.87
解释：
D is correct.
考点： Infer Credit Risk from Corporate Bond Prices
解析：
一年之后，债券变成了一年期的零息债券，
AA的值为 100/（1+1%+0.7%）=98.3284
A的值为100/（1+1%+1%）=98.0392
BBB的值为100/（1+1%+3%）=96.1538
预期值=5%*98.3284+85%*98.0392+10%*96.1538=97.8651
老师这道题未来三个评级的creadit 变化，假设债券面值1，△P=D*△y 的方式。因为是零息债券，D可以近似等于1.
先用PD* △P
85%*(1+0.7%)+10%*(1%+1%)+5%*(1%+0.7%)=2.19% 这里计算出来的相当于平均的价格未来的变化量。
再用1-2.19%算出来97.81% 这种计算逻辑对吗
