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水瓶公主 · 2023年03月07日

1.15euro/pound就是1pound=1.15euro吗？

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020021204000051

问题如下：

Consider a currency swap where interest on British pounds at the rate of 3% is paid and interest on euros at 2% is received. The British pound principal is 1.0 million pounds and the euro principal is 1.1 million euros. The most recent exchange has just occurred and the interest is exchanged every six months. There are two years are remaining in the life of the swap. The current exchange rate is 1.15 euro/pound. The risk-free rates in pounds and euros are 2.5% and 1.5%. Value the swap by considering it as the difference between two bonds. All rates are compounded semi-annually.

解释：

The swap involves exchanging

0.5 x 0.03 x 1,000,000 = 15,000 pounds with

0.5 X 0.02 X 1,100,000 = 11,000 euros with a final exchange of principal.

The value of the British pound

bond in British pounds is

15,0001  +  0.5  X  0.025\frac{15,000}{1\;+\;0.5\;X\;0.025}+15,000(1  +  0.5  X  0.025)2\frac{15,000}{{(1\;+\;0.5\;X\;0.025)}^2}+15,000(1  +  0.5  X  0.025)3\frac{15,000}{{(1\;+\;0.5\;X\;0.025)}^3}+1,015,000(1  +  0.5  X  0.025)4\frac{1,015,000}{{(1\;+\;0.5\;X\;0.025)}^4}=1,009,695

The value of the euro bond in euros is

11,0001  +  0.5  X  0.015\frac{11,000}{1\;+\;0.5\;X\;0.015}+11,000(1  +  0.5  X  0.015)2\frac{11,000}{{(1\;+\;0.5\;X\;0.015)}^2}+11,000(1  +  0.5  X  0.015)3\frac{11,000}{{(1\;+\;0.5\;X\;0.015)}^3}+1,111,000(1  +  0.5  X  0.015)4\frac{1,111,000}{{(1\;+\;0.5\;X\;0.015)}^4}=1,110,797

The value of the swap in British pounds is therefore

1,110,797 /1.15 - 1,009,695 = -43,785.

不是euro/pound=1.15吗

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1 个答案

DD仔_品职助教 · 2023年03月08日

嗨，努力学习的PZer你好：


同学你好，

答案没有问题哈，你可以换个角度来理解，举例子：

1.15 euro/pound代表1.15个euro可以买1个pound，那么1,110,797个euro，就可以买1,110,797 /1.15个pound。

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加油吧，让我们一起遇见更好的自己！

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