You visited the foreign exchange trading room of a major bank when a trader asked for quotes of the Japanese yen from various correspondents and heard of the following:
$:¥ quoted by JM Morgan: 102.30‒102.35.
$:¥ quoted by CitiBank: 102.25‒112.30.
$:¥ quoted by Wells Fargo: 102.35‒102.40.
Given the above rates, is there an arbitrage opportunity assuming no transaction costs? How are you going to exploit this arbitrage opportunity?
($:¥ quoted by CitiBank may be: 102.25‒102.30, but the professor didn't make any adjustment yet. So please leaves answer for each variable)
Yes, there is an arbitrage opportunity as the ask price of $:¥ by CitiBank is lesser than the bid price of $:¥ quoted by Wells Fargo.
We will give Wells Fargo 1,000,000$ and Wells Fargo would give us ¥102.35*1,000,000 = ¥102,350,000 for the current exchange rate of 102.35 (Bid price quoted by Wells Fargo)
Thus, we now have ¥102,350,000
We will now give these ¥102,350,000 to CitiBank for exchange with $ and we will get = $1,000,488.75 (at an exchange rate of 102.3 - Ask price quoted by CitiBank)
Hence the excess $488.75 is the arbitrage profit on an investment of $1,000,000
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