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Archie · 2022年05月07日

和上一题有什么区别

  1. FRM I
  2. Financial Markets And Products

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 X1.00751.0125\frac{1.0075}{1.0125}= 1.1443

1.15 X1.007521.01252\frac{1.0075^2}{1.0125^2}= 1.1387

1 .15 X 1.007531.01253\frac{1.0075^3}{1.0125^3}= 1 .1330

1.15 X1.007541.01254\frac{1.0075^4}{1.0125^4}= 1.1275

The exchanges are

The GBP value of the swap is

-5,3871  +  0.5  X  0.025\frac{5,387}{1\;+\;0.5\;X\;0.025}-5,340(1  +  0.5  X  0.025)2\frac{5,340}{{(1\;+\;0.5\;X\;0.025)}^2}-5,292(1  +  0.5  X  0.025)3\frac{5,292}{{(1\;+\;0.5\;X\;0.025)}^3}-29,592(1  +  0.5  X  0.025)4\frac{29,592}{{(1\;+\;0.5\;X\;0.025)}^4}= -43,785

不明白这两道题有什么区别，为什么之前一道题是每一期的差额折，这道题是另外一个算法，有啥区别

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1 个答案

DD仔_品职助教 · 2022年05月07日

嗨，从没放弃的小努力你好：


这俩题一模一样，只不过用了两种计算方法。

这个是currency swap涉及到了两个币种，英镑和欧元，上面展示的做法是把英镑和欧元的现金流分别计算出来折现，这样就得到了PV(英镑)和PV(欧元)，求他俩PV的差值，再转换一下汇率。

这里列举出来的方法是，先计算每个时间点上这俩币种的差额，同时转成一种货币，然后再把每一期的差额进行折现，求PV(差额)。

同学在这里掌握一种计算方法即可，挑你觉得简单的用，个人觉得第一种方便，因为只用转换一次币种，而下面这个方法每个时间点都要转换一次币种，更麻烦。

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加油吧，让我们一起遇见更好的自己！

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NO.PZ2020021204000052问题如下Consir a currenswwhere interest on British poun the rate of 3% is paianinterest on euros 2% is receive The British pounprincipis 1.0 million poun anthe euro principis 1.1 million euros. The most recent exchange hjust occurreanthe interest is exchangeevery six months. There are two years are remaining in the life of the swap. The current exchange rate is 1.15 euro/poun The risk-free rates in poun aneuros are 2.5% an1.5%. Value the swconsiring it the fferenbetween two bon. All rates are compounsemi-annually.Value the swabove consiring it a portfolio of forwarcontracts.p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.5px Helveticcolor: #454046}span.s1 {color: #4e5c70}span.s2 {color: #354567}span.s3 {color: #635148}The forwarrates corresponng to the exchanges times 0.5, 1.0, 1.5, an2.0 years are1.15 X1.00751.0125\frac{1.0075}{1.0125}1.01251.0075​= 1.14431.15 X1.007521.01252\frac{1.0075^2}{1.0125^2}1.012521.00752​= 1.13871 .15 X 1.007531.01253\frac{1.0075^3}{1.0125^3}1.012531.00753​= 1 .13301.15 X1.007541.01254\frac{1.0075^4}{1.0125^4}1.012541.00754​= 1.1275p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #443e42}p.p2 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #464048}p.p3 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #484348}p.p4 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #3f3841}p.p5 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #45414b}p.p6 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #464149}p.p7 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #46424b}p.p8 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #3f3842}p.p9 {margin: 0.0px 0.0px 0.0px 0.0px; font: 9.5px Helveticcolor: #4332}span.s1 {color: #63524span.s2 {color: #6f6b6b}span.s3 {font: 6.0px Helvetica}span.s4 {color: #435263}span.s5 {font: 6.0px Helveticcolor: #5a5256}span.s6 {color: #445f}span.s7 {font: 6.0px Helveticcolor: #445f}The exchanges arep.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.5px Helveticcolor: #474247}The Gvalue of the swis-5,3871  +  0.5  X  0.025\frac{5,387}{1\;+\;0.5\;X\;0.025}1+0.5X0.0255,387​-5,340(1  +  0.5  X  0.025)2\frac{5,340}{{(1\;+\;0.5\;X\;0.025)}^2}(1+0.5X0.025)25,340​-5,292(1  +  0.5  X  0.025)3\frac{5,292}{{(1\;+\;0.5\;X\;0.025)}^3}(1+0.5X0.025)35,292​-29,592(1  +  0.5  X  0.025)4\frac{29,592}{{(1\;+\;0.5\;X\;0.025)}^4}(1+0.5X0.025)429,592​= -43,785p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.5px Helveticcolor: #463f48}p.p1 {margin: 0.0px 0.0px 0.0px 0.0px; font: 8.5px Helveticcolor: #474246}span.s1 {color: #4b6f}老师好，能帮了看看我哪里计算错了吗？

2024-07-15 15:33 5 · 回答