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临江仙 · 2020年03月21日

问一道题：NO.PZ2020021204000051

  1. FRM I
  2. Financial Markets And Products

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.

选项：

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}+15,000(1  +  0.5  X  0.025)4\frac{15,000}{{(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}+11,000(1  +  0.5  X  0.015)4\frac{11,000}{{(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.

为什么折现的时候，没有加上本金，都是利息呢？

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1 个答案

品职答疑小助手雍 · 2020年03月22日

同学你好，计算结果其实是加了本金的，公式里没显示出来，我跟后台反馈下。

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