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xyrg+ · 2023年01月26日

如题

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  $  =0.009e0.0358×0.25+1.009e0.0374×0.5=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$  =0.01e0.0382×0.25+1.01e0.041×0.5=0.999411{l}B_{\;A\$}\;=0.01e^{-0.0382\times0.25}+1.01e^{-0.041\times0.5}\\=0.999411

lV=(0.9992270.999411÷1.2)×1,0000,000=166,385{l}V=(0.999227-0.999411\div1.2)\times1,0000,000=166,385

(1)0.009,1.009,0.01,1.01怎么来的?

(2)年末本金不回收吗,如果回收了在公式哪里表现了呢

(3)4%和3.6%没用到吗



2 个答案
已采纳答案

品职答疑小助手雍 · 2023年01月27日

同学你好,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。这种题不需要画现金流,把两个币种各自想成一个债券就行。

你的问题(3)4%和3.6%用到了,这是期初设置的交换的利息,后面还有半年也就是2期的互换,所以要用于计算问题(1)里你问的0.009,1.009,0.01和1.01,1单位的本金,对应的就是0.009美元和0.01澳元的利息,加上1是对应了期末要交换的本金这里对应问题(2)。

也就是说解析里是先假设面值为1对两只不同币种的债券进行了计算,票面利率分别为3.6%和4%、季度付息的半年期债券。求出债券与面值的关系后再通过汇率和实际的总面值来计算swap的价值

莫等闲2023 · 2023年09月24日

请问0.009美元和0.01澳元的利息如何计算,麻烦列一下计算公式,谢谢。

品职答疑小助手雍 · 2023年09月24日

注意是每季度付息,每次 1美元面值对应的 付息美元金额=1*3.6%/4=0.009。 澳元同样按利率计算即可。

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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?

2024-07-08 21:16 3 · 回答

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