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刘季松 · 2022年09月21日

请问为什么这里用连续复利求解呢,谢谢

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

请问为什么这里用连续复利求解呢,谢谢

3 个答案

李坏_品职助教 · 2023年11月01日

嗨,爱思考的PZer你好:


e^(−0.0358×0.25),这就是已经把年化利率折算成90天的利率了。如果是180天的利率那就乘以0.5进行折算。

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🧸苏小糖yb💚 · 2023年11月01日

r(90)可以直接用吗?不需要再折合成90天了吗

李坏_品职助教 · 2022年09月21日

嗨,努力学习的PZer你好:


这个是FRM考试默认的。如果考题没有明确规定用哪种复利,衍生品的计算题一般都用连续复利,这样计算的结果更精确一些。连续复利是假设每时每刻都一直在进行复利。


对于1年以内的合约,用离散复利算出来结果也很接近连续复利。如果期限长了,差异就大了。

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努力的时光都是限量版,加油!

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