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EthanL · 2024年08月24日

画图法

NO.PZ2023020101000015

问题如下:

Mafadi Consulting Limited is a boutique financial services company located in Johannesburg, South Africa. Mafadi specializes in providing commodity and currency hedging solutions to institutional investors and corporations.

Andre Fourie is a senior client services consultant for Mafadi. He manages relationships with a number of institutions to assist with their hedging needs. One of Fourie’s client’s is Global Bullion, a mining and exploration company headquartered in the United States.

Mbali Ndlovu, a trader on Mafadi’s derivatives desk, works closely with Fourie to implement solutions for his clients. Fourie asks Ndlovu to review and calculate the value of a five-year ZAR20,000,000 swap into which Global Bullion entered two years ago. It is a receive-fixed, Libor-based interest rate swap with annual resets (30/360 day count). The fixed rate in the swap contract established two years ago was 3%. Exhibit 1 estimates the present value factors.

Exhibit 1 Present Value Factors for Five-Year Swap

The value of Global Bullion’s swap contract is closest to:

选项:

A.

ZAR1,720,380.

B.

ZAR1,324,380.

C.

ZAR344,076.

解释:

Calculate the sum of PV = 0.9802 + 0.9560 + 0.9311 = 2.8673.

Calculate the fixed swap rate = (1 – 0.9311)/2.8673 = 0.0240.

Calculate swap value per ZAR = (0.0300 – 0.0240) *2.8673 = 0.0172.

Thus, total swap value = 0.01720 * ZAR20,000,000 = ZAR344,076.

老师,可以用画图法来解析一下这道题吗,不知道怎么解

1 个答案

李坏_品职助教 · 2024年08月24日

嗨,从没放弃的小努力你好:


画图法的计算过程(画图法就是向上箭头的fixed部分现金流现值 - 向下箭头的floating部分现金流的现值):


站在当前这个时刻,还剩3年到期,fixed部分的现金流现值 = 3%*NP*(0.9802+0.9560+0.9311)+NP*0.9311,NP是面值的意思。

floating部分的现金流现值 = NP,因为现在刚好处在annual reset的时刻(就是整数年份),所以float的价值就等于NP面值。


所以value of swap = fixed的现值 - floating的现值 = 3%*NP*(0.9802+0.9560+0.9311)+NP*0.9311 - NP,NP = ZAR 20 million,代入计算可得value = ZAR 342380, 和答案略有差距,差距来自于四舍五入。


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努力的时光都是限量版,加油!

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