NO.PZ202208160100000201
问题如下：
Based on the data in Exhibit 1, if a dealer quoted a bid–offer rate of CHF1.0741/EUR1.0746, then a profitable triangular arbitrage would most likely involve buying EUR1 from the dealer and then selling it in the interbank market for a profit of:
选项：
A.CHF0.0005.
B.CHF0.0008.
C.CHF0.0007.
解释：
Solution
A is correct. Calculate the CHF/EUR bid–offer cross rate implied by the interbank market using the equation CHF/EUR = (USD/CHF)–1 × USD/EUR = CHF/USD × USD/EUR. The equation shows that we have to invert the USD/CHF bid–offer quotes to get the CHF/USD bid–offer quotes.
First, given the USD/CHF quotes of 1.0453/1.0456, take the inverse of each and interchange the bid and offer, such that the CHF/USD quotes are (1/1.0456)/(11.0453) = 0.95639/0.95666 = 0.9564/0.9567.
Then multiply the CHF/USD and USD/EUR bid–offer quotes:
Bid: 0.9564 × 1.1241 = 1.07509 = 1.0751
Offer: 0.9567 × 1.1243 = 1.07562 = 1.0756
Thus, the CHF/EUR cross-rate implied by the interbank market is 1.0751/1.0756.
The dealer is posting an offer rate to sell the EUR at a rate below the interbank bid rate. Thus, triangular arbitrage would involve buying EUR from the dealer at 1.0746 (offer) and selling it in the interbank market at 1.0751 (bid) for a profit of CHF0.0005 (1.0751 – 1.0746) per EUR.
B is incorrect. It erroneously inverts the USD/CHF quotes but does not interchange the bid and offer and thus incorrectly calculates the interbank market cross rate.
Bid: 0.9567 × 1.1241 = 1.07543 = 1.0754
Offer: 0.9564 × 1.1243 = 1.07528 = 1.0753
Thus, the CHF/EUR cross-rate implied by the interbank market is 1.0754/1.0753. (Note that the bid is higher than the offer.)
Triangular arbitrage would involve buying EUR from the dealer at 1.0746 (offer) and selling it in the interbank market at 1.0754 (bid) for a profit of CHF0.0008 (1.0754 – 1.0746) per EUR.
C is incorrect. It erroneously inverts the USD/CHF quotes but incorrectly calculates the interbank market cross-rate by mixing up the cross bids and offers.
Bid: 0.9564 × 1.1243 = 1.07528 = 1.0753
Offer: 0.9567 × 1.1241 = 1.07543 = 1.0754
Thus, the CHF/EUR cross-rate implied by the interbank market is 1.0753/1.0754.
Triangular arbitrage would involve buying EUR from the dealer at 1.0746 (offer) and selling it in the interbank market at 1.0753 (bid) for a profit of CHF0.0007 (1.0753 – 1.0746) per EUR.
中文解析：
A是正确的。使用公式CHF/EUR = (USD/CHF) -1 × USD/EUR = CHF/USD × USD/EUR计算银行间市场隐含的CHF/EUR买卖交叉利率。公式表明，我们必须反转美元/瑞士法郎的买卖报价才能得到瑞士法郎/美元的买卖报价。
首先，假设美元/瑞郎的报价为1.0453/1.0456，取两者的逆并交换买入价和卖出价，这样瑞郎/美元的报价为(1/1.0456)/(11.0453)= 0.95639/0.95666 = 0.9564/0.9567。
然后乘以瑞士法郎/美元和美元/欧元的买卖报价:
竞价:0.9564 × 1.1241 = 1.07509 = 1.0751
卖出价:0.9567 × 1.1243 = 1.07562 = 1.0756
因此，银行间市场隐含的瑞郎/欧元交叉利率为1.0751/1.0756。
交易商以低于银行间买入价的价格卖出欧元。因此，三角套利将涉及以1.0746(卖出价)向交易商买入欧元，并以1.0751(买入价)在银行间市场卖出欧元，每欧元获利0.0005瑞郎(1.0751 - 1.0746)。
选项B不正确。它错误地反转了美元/瑞士法郎的报价，但没有交换买入价和卖出价，因此错误地计算了银行间市场交叉利率。
竞价:0.9567 × 1.1241 = 1.07543 = 1.0754
卖出价:0.9564 × 1.1243 = 1.07528 = 1.0753
因此，银行间市场隐含的瑞郎/欧元交叉利率为1.0754/1.0753。(请注意，出价高于出价。)
三角套利包括以1.0746(卖出价)向交易商买入欧元，并以1.0754(买入价)在银行间市场卖出，每欧元获利0.0008瑞郎(1.0754 - 1.0746)。
C是不正确的。它错误地颠倒了美元/瑞士法郎的报价，但由于混淆了交叉买入价和卖出价而错误地计算了银行间市场的交叉利率。
竞价:0.9564 × 1.1243 = 1.07528 = 1.0753
卖出价:0.9567 × 1.1241 = 1.07543 = 1.0754
因此，银行间市场隐含的瑞郎/欧元交叉利率为1.0753/1.0754。
三角套利包括以1.0746(卖出价)向交易商买入欧元，并以1.0753(买入价)在银行间市场卖出，每欧元获利0.0007瑞郎(1.0753 - 1.0746)。
老师请看看我这么做有什么问题
dealer 报价：CHF/EUR 1.0741-1.0746
银行间报价：USD/EUR 1.1241-1.1243
USD/CHF 1.0453-1.0456
推导出银行间CHF/EUR 1.0751-1.0756,所以从dealer处买欧元
如果现在有1元CHF，可以在dealer处买1/1.0746EUR，现在手上有了欧元，可以在银行间市场卖欧元买美元，于是就是1/1.0746*1.1241，然后再在银行间市场卖美元买CHF，就是1/1.0746*1.1241/1.0456=1.000443，减1后最接近选项a
