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Amy · 2021年04月07日

复利的方法还是分不清楚，可以帮我总结一下吗？

  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.

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}+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.

老师上课的时候总结了4中复利方法，这四种复利方法分别会对应哪种问法呀？1.LIBOR。2.Rf（年复利）。3.Rf（Bond,Sport rate).4.Rf连续复利。就是在题目中分别看到什么可以对应这4种方法啊？这道题我以为是用年复利的方法，结果是Bond/SR的。特别晕！

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1 个答案

袁园_品职助教 · 2021年04月08日

同学你好！

这道题题目说了All rates are compounded semi-annually.也就是都是半年复利一次

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