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Zunniyaki · 2022年12月12日

互换的名义本金应设定为使得公司获得的浮动收益与其必须支付的浮动息票收益相等的金额

  1. CFA III
  2. Derivative

NO.PZ2018113001000080

问题如下：

Roderick is the chief financial officer of a chocolate company. A year ago, the company issued floating rate bonds. Roderick now expects interest rates to rise and remain high levels for the next two years. Over the next two years, Roderick wants to use interest-rate swaps to effectively convert floating-rate bonds into fixed-rate payments.

Explain how Roderick would construct this swap from the following perspectives:

i: tenor

ii: the cash flow of the swap

iii: the notional value of the swap

iv. settlement dates

选项：

解释：

Answer:

i: The swap term is two years, in line with the length of time for which Roderick expects rates to stay high.

ii: Roderick will establish an interest rate swap in which Roderick will receive payments based on a floating reference rate and will make payments based on a fixed rate. The source of the reference rate and the value of the fixed rate will be determined at the commencement of the swap.

For Roderick, the net effect of receiving fixed payments and making floating payment in the swap for his coupon bonds is to convert his floating obligation to pay a fixed obligation. This situation will benefit Roderick if Tioga's expectations of higher interest rates are realized.

iii: The notional value of the swap should be set such that the floating payments that Wyalusing receive will equal the float coupon payments that Wyalusing must make on its float-rate bond obligations.

v. Swap settlement dates should be set on the same days as the float-rate bond’s coupon payment dates.

中文解析：

本题考察的是利用利率互换来改变负债的性质。

一年前，公司发行了浮动息票债券。Roderick现在预计利率将会上升，并在未来两年内保持在高位。在这两年期间，Roderick希望使用利率互换来有效地将浮动利率债券的息票支付转换为固定利率支付。这样在高利率水平下，支付的票息就会下降，对公司有利。

该互换需要满足以下四点：

1. 需要进入一个收到浮动支付固定的互换中。其中互换的期限是两年，和预测的高利率维持的时间一样长；

2. 是作为收到浮动支付固定的一方，并且使得收到的浮动和在原来浮动利率债券中支付的浮动一样，从而相互抵消，将其债券息票支付的浮动义务转换为支付固定的义务。在这种情况下如果Roderick的高利率预期得以实现，将使公司受益。

3. 互换的名义本金应设定为使得公司获得的浮动收益与其必须支付的浮动息票收益相等的金额。

4. 互换的结算日期应与浮动利率债券的息票支付日期相同。

老师您好，关于这句话的意思，不是让互换的名义本金和该公司发行的浮动利率债券的面值一样吧？根据公式MDURt*MVp=MDURp*MVp+NPs*MDURs，那么swap的notional principal不是取决于swap的duration么？

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Hertz_品职助教 · 2022年12月13日

嗨，从没放弃的小努力你好：


同学你好

1. 老师您好，关于这句话的意思，不是让互换的名义本金和该公司发行的浮动利率债券的面值一样吧？

——对的，互换的名义本金应该是和这个债券的面值一样。这样表述是最确切的，这里是默认互换中浮动端的利率和债券的浮动利率是一样的，因此保证互换的浮动端金额和债券的浮动利息相等，本质上就是保证互换的名义本金和债券面值一样。

2. 根据公式MDURt*MVp=MDURp*MVp+NPs*MDURs，那么swap的notional principal不是取决于swap的duration么？

——不是的哦，不要这样理解。

从利率互换它诞生的原因（就是改变loan的性质，比如将原来的浮动贷款变成固定贷款等）我们才能很清楚的知道互换的名义本金一定是要和loan的金额相等的，而且是仅仅取决于要改变的loan的金额。

相应的如果这个loan的本金是不断变化的，对应的互换的名义本金就要随之变动。总之原则就是名义本金和loan的金额匹配，对应本题就是和债券的面值匹配。

上面这个公式是说名义本金和久期是有这样的关系的，但是并不是决定的关系哦。

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