NO.PZ2021061002000052
问题如下：
QWR is a financial intermediary active in
both futures and forward markets. At time t = 0, QWR observes the following
zero rates over three periods:
About the three-period par swap rate (S3), Which of the following descriptions is correct?
选项：
A. Because the swap rate represents the fixed
rate at which the present value of fixed and future cash flows equal one
another, we can first use zero rates to solve for the implied forward rate per
period, then discount each implied forward rate back to the present using zero
rates, and solve for s3 to get 3.46%.
B. Because the swap rate represents the fixed
rate at which the present value of fixed and future cash flows equal one
another, we can use zero rates to discount each zero rate back to the present,
and solve for s3 to get 3.02%.
C. Because the swap rate represents the fixed
rate at which the present value of fixed and future cash flows equal one
another, we can first use zero rates to solve for the implied forward rate per
period, then discount each zero rate back to the present using implied forward
rates, and solve for s3 to get 3.99%
解释：
中文解析
本题考察的实际是“脱靴（bootstrapping）”的过程。
具体计算如下：
先根据下面的公式计算出：
IFR0,1 = 2.52%, IFR1,1 = 3.56%, and IFR2,1 = 4.43%
然后再按照下面的公式计算S3：
最终得到S3 =3.46%，选A。
前面到3个IFR的计算可以理解。但S3恒等式的左侧，0-1，1-2，2-3分区间并按照区间利率进行折现，为何是折现后相加等于右侧呢。
