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Ponybear · 2023年11月25日

为什么不可以用F/S=(1+0.45%*90/360)/(1+0.6%*90/360)公式呢?

NO.PZ2018091706000044

问题如下:

BBQ firm is an American company and exported steel to a firm which is in England. For some reasons, BBQ will receive the payment of 3,600,000 GBP in six months and the firm would change these pounds into dollars. To hedge the currency risk, BBQ enters a 6 month forward contract to sold GBP at 1.5512USD/GBP

Three months passed. Now, the spot exchange market rate is 1.5500 USD/GBP for bid and 1.5505 for ask .The firm collects the forward rates and 90-Day Libor in the following tables:

According to the above information, the mark-to-market value for BBC’s forward position is closest to:

选项:

A.

USD 324.

B.

USD -323.64.

C.

USD 323.64.

解释:

C is correct.

考点Mark to-Market Value

解析BBQ公司进入了一份时长6个月的外汇合约它担心卖出GBP贬值所以该合约是卖GBPUSD即在合约到期时公司要以1.5512USD/GBP的价格卖出GBP现在过去三个月那么截止当前该合约还剩3个月到期由于3个月后公司需要进入一份与期初头寸相反的对冲合约来结束期初的合约所以那时BBQ应该买入GBP卖出USD买入GBP就需要以做市商的卖价ask买入所以我们求得未来3个月 USD/GBP的市场报价1.5505 +0.00061=1.55111

由于买价是1.55111卖价是1.5512所以3,600,000 GBP的本金在合约到期时的利润就是1.5512-1.55111×3,600,000 = 324USD但是这个数值是到期时合约的价值,我们对其往前折现3个月才能求得合约在当前的价值本题中的标价货币是USD所以折现时候需要使用USD3个月利率水平USD 3241+0.0045(90/360)=USD 323.64\frac{USD\text{ 324}}{1+0.0045{(90/360)}}=USD\text{ }323.64

然后S是3个月时Spot的价格1.5505 求得6个月时点的F 这个F不等于1.55111,这是为什么呢?

1 个答案

笛子_品职助教 · 2023年11月26日

嗨,从没放弃的小努力你好:


为什么不可以用F/S=(1+0.45%*90/360)/(1+0.6%*90/360)公式呢?

同学给出的公式,是covered 利率平价知识点。

而这道题涉及的知识点是: mark-to-market value。


mark-to-market value 有自己的固定解法。

我们不能用covered利率平价的知识点去解mark-to-market value 的题。


然后S是3个月时Spot的价格1.5505 求得6个月时点的F 这个F不等于1.55111,这是为什么呢?

如果S和F之间不存在与利率的对应关系的话,说明不满足covered 利率平价。



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