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hanfei · 2023年09月21日

关于本金和利息的交换方向

  1. FRM I
  2. Financial Markets And Products

NO.PZ2019052801000050

问题如下：

A US company entered into a one-year currency swap with quarterly reset six months ago. The notional principle is $1,000,000, At the swap’s initiation, the US company receives the notional amount in Australian dollars and pays to the counterparty the notional amount in US dollars. At the swap’s expiration, the US company pays the notional amount in Australian dollars and receives from the counterparty the notional amount in US dollars.The annual fixed swap rates for Australian dollars is 4% and for US dollars is 3.6%.The current spot exchange rate is A$1.2 / $ .

The US term structure is:

  • r(90)=3.58%

  • r(180)= 3.74%

The Australian term structure is:

  • r(90)=3.82%
  • r(180)= 4.1%

What is the value of the currency swap to US company?

选项：

A.

$-142,145million.

B.

$142,145million.

C.

$166 ,385.

D.

$-166 ,385.

解释：

C is correct.

考点：货币互换估值.

解析：

美国公司收美元本金和利息的价值：

lB  $  =0.009e−0.0358×0.25+1.009e−0.0374×0.5=0.999227{l}B_{\;\$}\;=0.009e^{-0.0358\times0.25}+1.009e^{-0.0374\times0.5}\\=0.999227

美国公司支澳大利亚元本金和利息的价值：

lB  A$  =0.01e−0.0382×0.25+1.01e−0.041×0.5=0.999411{l}B_{\;A\$}\;=0.01e^{-0.0382\times0.25}+1.01e^{-0.041\times0.5}\\=0.999411

lV=(0.999227−0.999411÷1.2)×1,0000,000=166,385{l}V=(0.999227-0.999411\div1.2)\times1,0000,000=166,385

老师按照基础班讲义的238和239页的原理来说，美国公司在期初收A，付USD；在期末就要付A，收美元；老师上课的时候说本金的交换方向和收利息的方向是反过来的嘛，但是这里为啥本金和利息的折现都是同一个方向呢？

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2 个答案

品职答疑小助手雍 · 2023年09月25日

不用考虑期初的，因为这是过去的事情了。

只要考虑期间和期末要付的A就可以了

另一端只考虑要收的USD。

这样两端相当于就是两只债券啊，现金流都是同向的。

品职答疑小助手雍 · 2023年09月22日

同学你好，上课说的反过来是期初和后期还款反过来，也就是：

期初收A，付USD；期间到期末就要付A利息和本金，收美元利息和本金。

其实货币互换就是分别把收付两端都当成一个债券看就可以了。

hanfei · 2023年09月25日

”其实货币互换就是分别把收付两端都当成一个债券看就可以了“，这句话我能理解， 但是关于 期初收A，期间和期末付A，A债券的一个收一个付，现金流方向不一样为啥能够用同一个方向进行折现估值呀？ 能再解释一下吗，感谢

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