Suppose Lufthansa receives the following indirect quotes in the currency markets of New York. They are €0.92-3/U.S.$. Given the quotes, there may or may not be arbitrage opportunities if you were a currency trader in Paris
What range of £/€ bid and ask quotes would motivate you to arbitrage the currencies? Explain.
Answer: This may be an opportunity for triangular arbitrage in Paris, and there may be two ways to conduct the trades. In the first way, as a currency trader in Paris, you would convert from euros to U.S. dollars at the ask rate. Once this is accomplished you would convert from dollars to pounds at the bid rate. In the second way you would convert from pounds to dollars at the ask rate, then from dollars to euros at the bid rate. The first quote gives the bid price for the euro in terms of the pound and the second quote yields the ask price. Using the given rates, Lufthansa would end up with the following amounts. From euros to pounds equals €.93/$ (ask) x $(1/0.63) /£ (bid) which equals €1.4762/£. From pounds to euros equals £0.64/$ (ask) x $(1/0.92/€) (bid) which equals €1.4375/£. It appears that Lufthansa can buy pounds in New York for €1.4762/£, which is the equivalent of selling euros at a rate of £0.6774/€. So, if Lufthansa can buy euros in Paris for less than €1.4762/£, it can arbitrage profit.
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