# Arbitrage between markets

I'm trying to understand how arbitrage works, but I'm having some difficulties based on some restrictions:

• I have markets A, B and C.
• The currencies that are traded are X <-> Y, and X <-> Z.
• The only thing that can be transferred between markets A, B and C is currency X.
• The time it takes to transfer the funds (in currency X) between any market is about 2-10 minutes.
• The opportunity for arbitrage last for about 1 hour.

The exchange rates on market A

• 1 X exchanges for 3.22 Y
• 1 X exchanges for 5.11 Z

The exchange rates on market B

• 1 X exchanges for 3.25 Y
• 1 X exchanges for 5.07 Z

The exchange rate on market C

• Does not exchange X <-> Y
• 1 X exchanges for 4.98 Z

Suppose that exchange A is the exchange with the highest volume and presumably the most accurate exchange rate. How can one take advantage of the arbitrage opportunities if the only thing that can be transferred between exchanges is currency X and it takes 2-10 minutes?

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Have you looked at Triangular Arbitrage? en.wikipedia.org/wiki/Triangular_arbitrage – Quant Guy Apr 25 '12 at 2:32
@QuantGuy yes, but that presumes that if that you can "easily" take your currency between adjacent markets in currency other than X. In the situation I'm exploring, it's only feasible to move currency X between the markets, which seems to defeat the purpose of arbitrage (or at least that's how I see it). – Lirik Apr 25 '12 at 2:40

First, express the prices of Y and Z in terms of X, and let's rename X "\$" for convenience's sake. Then Y costs about \$0.311 in market A and \$0.308 in market B. Assuming no bid/ask spread, therefore you should buy Y in B and sell it in A. Z costs \$0.196, \$0.197, \$0.201 in A, B, and C, respectively, so buy Z in A and sell it in C. Since money (X) is transferable between markets, you can use one market as a funding source for another, so that all arbitrages can be set up to have zero cost at inception.