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SHAO · 2023年11月14日

老师，请教

  1. CFA II
  2. Derivative

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？

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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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