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· 2022年03月09日

请问是否省略了一个*1？

  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：

期初和期末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

期初和期末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

（Vusd-Vaud/1.2)*NP*year

请问这里是不是省略了year=1呢？有点疑惑期限的问题，题目中说六个月之前加入的，合同总共一年，所以还剩下半年时间，不应该乘以0.5嘛？

谢谢解答~

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1 个答案

品职答疑小助手雍 · 2022年03月09日

同学你好，前面两笔折现的已经分别对0.25年和0.5年的现金流进行了处理，最后一步相减的就是站在已经过了6个月，还剩6个月的节点上的PV的差额了。

这一步不用乘以年份，不存在省不省略的问题。

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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 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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