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Ray12 · 2023年10月03日

请问这里C为什么不2%/2=1%?

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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.

B.

-$781,323.

C.

-$181,323.

解释:

B is correct.

The value of an equity swap at time t is calculated as

VEQ,t=VFIX(C0)(StSt1)NAEPV(ParNAE)PV(ParNAE)V_{EQ,t}=V_{FIX}(C_0)-(\frac{S_t}{S_{t-1}})NA_E-PV(Par-NA_E)-PV(Par-NA_E)

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。

如题,请问这里C为什么不2%/2=1%?

1 个答案
已采纳答案

pzqa35 · 2023年10月04日

嗨,爱思考的PZer你好:


题目中的已知条件为fixed swap rate是2%,根据fixed swap rate的计算公式我们可以看出这不是一个年化的利率,所以不需要除以2哈.


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