问一道题：NO.PZ201710020100000104

问题如下：

4. Based on Exhibits 1, 2, and 3, the mark-to-market gain for Goldsworthy’s forward position is closest to:

选项：

GBP 20,470.

GBP 20,500.

GBP 21,968.

解释：

A is correct.

Marking her nine-month contract to market six months later requires buying GBP/EUR three months forward. The GBP/EUR spot rate is 0.7342/0.7344, and the three-month forward points are 14.0/15.0. The three-month forward rate to use is 0.7344 + (15/10000) = 0.7359. Goldsworthy sold EUR 5,000,000 at 0.7400 and bought at 0.7359. The net cash flow at the settlement date will equal EUR 5,000,000 × (0.7400 – 0.7359) GBP/EUR = GBP 20,500. This cash flow will occur in three months, so we discount at the three-month GBP Libor rate of 58 bps:

$\frac{GBP20,500}{1+0.0058\lbrack90/360\rbrack}=GBP20,470.32$

考点：Mark –to-Market Value

解析：计算Market-to-Market Value的方法就是在当前时刻签订一笔反向对冲合约。

投资者在6个月前先签订了一份长达9个月的合约， 这份合约准许投资人以GBP/EUR=0.7400的价格卖出EUR.
现在过去6个月的时间，该份合约还剩3个月到期，那么我们在当前时候就要签订一份时长为3个月的买EUR的合约。

注意到表二中提供了3个月的汇率远升水情况。据此，我们可以求得未来三个月的远期汇率，由于反向对冲合约是在未来3个月买入EUR,所以要求DEALER的卖价，即：

ASK:0.7344 + (15/10000) = 0.7359

投资者以0.7359的价格买入EUR,并且以0.7400的价格卖出EUR，并且本金是5,000,000EUR，所以合约为投资者带来的收益是5,000,000 × (0.7400 – 0.7359) GBP/EUR = GBP 20,500. 但是注意到这里的收益是发生在合约到期时的收益，而 Mark – to-Market Value要求的是当前时刻的收益，所以我们还要对GBP 20,500进行折现，折现的期限就是3个月。在本题中，收益是以GBP形式表现的，所以折现利率应该选用GBP的3个月的利率水平。于是得到：

$\frac{GBP20,500}{1+0.0058\lbrack90/360\rbrack}=GBP20,470.32$