Three-point forex arbitrage (also known as triangular forex arbitrage), is totally risk free forex trading theory. It could be called a strategy, although implementing it is almost impossible.
As the name suggests three-point arbitrage involves trading of three currency pairs almost simultaneously so as to exploit any insufficiency of pricing while it still exists. Three-point forex arbitrage opportunities do not occur every so often, and if they do, they only last for seconds. To take advantage of this type of forex arbitrage opportunity, one needs to have sophisticated computer equipment and/or programs for the automation of the process.
Three-point forex arbitrage works as follows. Given 3 currencies (a, b, and c), three possible currency exchange rates exist: S(a/b), S(a/c) and S(b/c). Three-point forex arbitrage is consistent if:
| Condition (1): | S(a/b)= | S(a/b) | |||||||||||||||
| S(b/c) |
Three-point forex arbitrage consists of two steps: (i) checking out if condition (1.0) is violated or not; and (ii) determining the profitable sequence. Assuming that the no-arbitrage state is violated such that S(a/b) > S(a/c)/ S(b/c), we are able to determine the gainful sequence with the help of a triangle by randomly placing each one of the three currencies at the corners of the triangle.
Profitable and unprofitable sequences in three-point forex arbitrage
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| (i) Unprofitable sequence | (ii) Profitable sequence |
| figure (1.1) | |
The Sequence of Profitable Forex Arbitrage
To find out the gainful sequence in a triangular forex arbitrage, we start by one of the 3 currencies, moving clockwise around the triangle until we end up at the point of start, with the same currency. If the final currency is less than one unit compared to the one we started with, a loss will be made (figure 1.1 (i))
(i) Selling a and buying b to obtain 1/[S(a/c)] units of c.
(ii) Selling c and buying b to obtain S(b/c)/[S(a/c)] units of b.
(iii) Selling b and buying a to obtain S(b/c) S(a/b)/[S(a/c)] units of a.
A forex arbitrage profit will therefore be made by moving in the opposite direction (figure 1.1 (ii)
(i) Selling a and buying b to obtain 1/[S(a/b)] units of b.
(ii) Selling b and buying c to obtain 1/[S(a/b)S(b/c)] units of c.
(iii)Selling c and buying a to obtain S(a/c)/[S(a/b)S(b/c)] units of b.
In general, if condition (1.0) is violated, a forex arbitrage profit can be made in moving a certain direction and a loss will result by moving in the opposite direction.