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梦梦 · 2024年07月08日

两个问题

  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

1、“本题是1年期的swap，每季度交换一次，已经过了半年了，求value的问题”求的不是0时刻签约的value？那是求1年到期，现在的value？

2、FRM考试只要给了利率没说怎么计息，就用连续复利吗？

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3 个答案
已采纳答案

李坏_品职助教 · 2024年07月16日

嗨，爱思考的PZer你好：


（1+r/2）^1，（1+r/2）^2，这个就是离散复利啊。


只要题目没有必须要求用continuously compounding，那就可以用这种离散复利。r/2是指按照半年复利，如果是按照季度复利那就是r/4.

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努力的时光都是限量版，加油！

梦梦 · 2024年07月16日

好的，谢谢

李坏_品职助教 · 2024年07月15日

嗨，努力学习的PZer你好：


用离散复利也可以，误差是非常小的，不会影响做题。


如果题目说continuously compounding，那就必须用连续复利。如果啥也没说，那就可以用离散复利。

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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！

梦梦 · 2024年07月16日

还有一问您没回答，一般题目怎么表述时，是用求债券的方式折现？比如（1+r/2）^1，（1+r/2）^2这种？

李坏_品职助教 · 2024年07月09日

嗨，从没放弃的小努力你好：


题目开头说了“six months ago”，意思是6个月之前就签订了这个swap，所以现在是在0时刻往后的第6个月。问你现在的swap value是多少。


连续复利与离散复利在期限较短的情况下，几乎没有误差。你用任何一种计算方法都不会影响你选出正确答案的。

基础班课件里的例题用的就是离散复利的形式，也可以。


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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！

梦梦 · 2024年07月10日

好的，谢谢

梦梦 · 2024年07月15日

老师好，这道题“quarterly reset six months ago”，用离散复利也可以吗？（1+r（90））^0.25，（1+r（180））^0.5？一般题目怎么表述时，是用求债券的方式折现？比如（1+r/2）^1，（1+r/2）^2这种？

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NO.PZ2019052801000050 问题如下 A US company entereinto a one-yecurrenswwith quarterly reset six months ago. The notionprinciple is $1,000,000, the swap’s initiation, the US company receives the notionamount in Australillars anpays to the counterparty the notionamount in US llars. the swap’s expiration, the US company pays the notionamount in Australillars anreceives from the counterparty the notionamount in US llars.The annufixeswrates for Australillars is 4% anfor US llars 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 Australiterm structure is: r(90)=3.82% r(180)= 4.1%Whis the value of the currenswto US company? A.$-142,145million. B.$142,145million. C.$166 ,385. $-166 ,385. 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}\\=0.999227lB$​=0.009e−0.0358×0.25+1.009e−0.0374×0.5=0.999227美国公司支澳大利亚元本金和利息的价值lB  A$  =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}\\=0.999411lBA$​=0.01e−0.0382×0.25+1.01e−0.041×0.5=0.999411lV=(0.999227−0.999411÷1.2)×1,0000,000=166,385{l}V=(0.999227-0.999411\v1.2)\times1,0000,000=166,385lV=(0.999227−0.999411÷1.2)×1,0000,000=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US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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