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JYJY · 2022年08月31日

为什么是GBP minus basis？

  1. CFA III
  2. Derivative

NO.PZ2018113001000081

问题如下：

A British chocolate company wants to set up a branch in the United States. Since the company is in a better position to borrow at home, it is planning to borrow GBP at home and use currency swaps to convert them into dollars as needed.

Describe how this cross-currency basis swap should be structured from the beginning, period and end of the swap.(Suppose the basis is quoted on the non-USD leg of the swap)

选项：

解释：

Answer:

At inception, the chocolate company will pay the notional principal of GBP and will receive an amount of USD according to the USD/GBP exchange rate, agreed to at inception.

At each payment date, the chocolate company will receive interest in GBP and will pay interest in USD. Both payments are based on floating reference rates for their respective currencies. The GBP rate will also include a basis rate that is quoted separately. On each settlement date, the chocolate company will receive an amount of GBP based on the GBP floating rate minus the basis rate applied to the swap notional value, and it will pay an amount of USD based on the USD floating rate and the USD/GBP exchange rate that was set at inception

At maturity, the cash flows at maturity are the inverses of the cash flows at inception.The chocolate company will receive the notional principal of GBP and will pay an amount of USD based on the USD/GBP exchange rate that was set at the beginning, applied to the GBP notional principal.

中文解析：

本题考察的是cross-currency basis swap。

一家英国的巧克力公司要在美国设立一个分公司，因此需要美元。英国的公司在英国借款更有优势，利率更低，因此他在本国借GBP，再通过cross-currency basis swap将其转换为USD。

期初：将约定一个在期初和期末交换名义本金时使用的汇率，然后该公司将支付GBP的名义本金，并根据约定好的这个汇率收到对应金额的美元本金。

期间：在每个互换日，该公司将收到GBP利息，并支付美元利息，支付和收到的利息都是基于各自币种的浮动利率和名义本金来计算的，另外收到的GBP利率中包括一个basis。因此在每个结算日期,该公司都将收到基于GBP的浮动利率-basis计算出来的利息金额,同时支付一笔基于美元的浮动利率和美元本金计算出来的美元利息。

期末：和期初的现金流方向相反，将会收到一开始换出去的GBP，同时支付一开始时收到的美元金额。结束整个互换。

On each settlement date, the chocolate company will receive an amount of GBP based on the GBP floating rate minus the basis rate applied to the swap notional value


题目里假设basis是在nonUSD leg 那不是应该rGBP=GBP floating rate + basis吗

按照答案如果是minus 那不就相当于是加在了USD leg上与题目假设相违背了

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Hertz_品职助教 · 2022年09月01日

嗨，爱思考的PZer你好：


同学你好

我明白同学的疑惑了哈，是这样的：

1.     首先呢， Cross currency basis swap是一种特殊的互换，特殊之处一是在于互换双方在互换期间互相付给对方的利率默认都是浮动利率，并且会随着某一个币种的升贬情况，或者其他情况，在互换的一方加上一个basis来调节一方支付给另一方的利率。——（回答同学的第一个提问）

而在cross currency basis swap中，默认basis是跟着非美元一端的，所以在咱们这里的互换，basis是跟着英镑GBP的；

2.     为什么是minus basis呢？

这其实是一种表达方式，学习的是教材的表达，像本题这种我们自己来描述互换的题目，我们也可以写floating rate add basis，就是写加上basis。这一点都没有关系。

因为basis本身是可正可负的，所以是minus还是add都可以实现相同的加上或者减掉basis的效果。

只不过习惯的表述为minus basis。就像我们在一些互换中浮动利率常用MRR来表示一样的。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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