NO.PZ202108100100000204
问题如下：
From the bank’s perspective, using data from Exhibits 4 and 5, the fair value of the equity swap is closest to:
选项：
A.-$1,139,425.
-$781,323.
-$181,323.
解释：
B is correct.
The value of an equity swap at time t is calculated as
The swap was initiated six months ago, so the first reset has not yet passed; thus, there are five remaining cash flows for this equity swap. The fair value of the swap is determined by comparing the present value of the implied fixed- rate bond with the return on the equity index. The fixed swap rate of 2.00%, the swap notional amount of $20,000,000, and the present value factors in Exhibit 5 result in a present value of the implied fixed-rate bond’s cash flows of $19,818,678:
The value of the equity leg of the swap is calculated as (103/100)($20,000,000) = $20,600,000
Note the swap’s notional amount and the implied fixed-rate bond’s par value are both $20,000,000; therefore, the term – PV(Par – NAE ) reduces to zero.
The swap was designed to profit if rates fell or equities declined. Neither happened, so the swap value will be negative for the bank. The fair value of the
equity swap, from the perspective of the bank (receive-fixed, pay-equity party)
is calculated as
VEQ = $19,818,678 - $20,600,000 = -$781,322
中文解析：
本题考察的是equity swap的估值。
这里的头寸是收固定付equity return。
因此在t时刻的value，即为互换中隐含的固定利率债券在t时刻的价值-权益端在t时刻的价值。需要注意权益端价值的计算为 (103/100)($20,000,000) = $20,600,000。
课程中讲的是equity swap的期初、末的本金不用互换，但题目中103/100 x NP和fix coupon折现时均考虑了本金折现
