梦梦 · 2024年07月15日

swap例题哪里计算错了？

NO.PZ2020021204000052

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.

Value the swap above by considering it as a portfolio of forward contracts.

解释：

The forward rates corresponding to the exchanges at times 0.5, 1.0, 1.5, and 2.0 years are

1.15 X $\frac{1.0075}{1.0125}$ = 1.1443

1.15 X $\frac{1.0075^2}{1.0125^2}$ = 1.1387

1 .15 X $\frac{1.0075^3}{1.0125^3}$ = 1 .1330

1.15 X $\frac{1.0075^4}{1.0125^4}$ = 1.1275

The exchanges are

The GBP value of the swap is

- $\frac{5,387}{1\;+\;0.5\;X\;0.025}$ - $\frac{5,340}{{(1\;+\;0.5\;X\;0.025)}^2}$ - $\frac{5,292}{{(1\;+\;0.5\;X\;0.025)}^3}$ - $\frac{29,592}{{(1\;+\;0.5\;X\;0.025)}^4}$ = -43,785

老师好，能帮了看看我哪里计算错了吗？

添加评论

5 个答案

已采纳答案

李坏_品职助教 · 2024年07月16日

嗨，从没放弃的小努力你好：

这个题目不一定是0时刻，只是说这个currency swap还剩2年到期，半年交换一次现金流，所以还剩下4次现金流交换。

Value the swap above by considering it as a portfolio of forward contracts.

意思是要想把这个货币互换看做一系列外汇远期合约的组合。所以需要先求出每一个时间点对应的不同的远期汇率：

再把用远期汇率全部转化为英镑去作差。

而题目条件告诉我们“ The risk-free rates in pounds and euros are 2.5% and 1.5%.”，既然已经转化为英镑了，折现的利率就用英镑的2.5%即可。由于是每半年交换一次现金流，所以是-5387/(1+0.5*0.025), -5340/(1+0.5*0.025)^2 ……

----------------------------------------------
加油吧，让我们一起遇见更好的自己！