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SHAO · 2023年11月14日

老师,请教

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,不太明白题目的解题思路是什么,0.03和0.024都是fixed swap rate吗?

3 个答案
已采纳答案

李坏_品职助教 · 2023年11月16日

嗨,从没放弃的小努力你好:


这道题是每年进行一次利率重置,所以每个整数年份的floating现值都等于NP,这个是floating的规律。不用再乘以0.9560了。


假如不是在利率重置的时刻,那么floating的现值 = NP + 下一笔利息的present value = NP + 利息×present value factor

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

李坏_品职助教 · 2023年11月15日

嗨,努力学习的PZer你好:


对 我这个算法实际上是老师课上说的画图法,比较简单。


答案解析实际上是重新定价法,是课上讲的另一种算法,比较复杂。里面的2.4%指的是当前的swap rate,它是用 0.9802 和 0.9560 以及 0.9311这三个present value factor计算的。


重新定价法的核心就是要找到当前的Swap rate(2.4%), 再用初始时刻的swap rate(3%)减去2.4%,再乘以 sum of PV和面值。

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努力的时光都是限量版,加油!

李坏_品职助教 · 2023年11月14日

嗨,努力学习的PZer你好:


题目中说了“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.” 意思是这个Swap是5年期的,但是它是在2年前就签订了,也就是说现在还剩3年到期。现在让你计算当前这个Swap的Value。


The fixed rate in the swap contract established two years ago was 3%. 意思是2年前签订合约的时候,swap rate是3%. 也就是swap的fixed interest是按照3%计利息的。


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,这里的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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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

SHAO · 2023年11月15日

老师,按您的计算方法没有用到2.4%哎,这个2.4%是什么呀,现在的swap rate(fixed)吗?

SHAO · 2023年11月16日

老师,上述回答中“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。” 请问这句话的意思是,每个整数年份的float现值都等于NP吗?这里已经过去两年了,他的现值不应该是NP/0.9560吗?

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