A triangular arbitrage opportunity exists if either of these conditions is violated:
To determine whether a triangular arbitrage opportunity exists, follow these steps:
Example: Consider an interbank quote of 85.76/85.80 on the currency pair A/B. The dealer quotes on the same currency from three dealers are as follows:
Dealer 1 quote: 85.74/85.81
Dealer 2 quote: 85.73/85.75
Dealer 3 quote: 85.81/85.83
When assessing for triangular arbitrage, we suggest using a ‘number line’ format, where the interbank and dealer rates are represented along a number line:
Write the interbank rate within two lines as follows:
| 85.76 85.80 |
Write all dealer quotes with reference to the interbank quote within the two lines. So, a number less that 85.76 would appear to the left of the interbank quote whereas a number greater than 85.80 would appear to the right of the interbank quote. The three dealer quotes can be represented as follows:
| Interbank quote | 85.76 85.80 | ||
| Dealer 1 quote | 85.74 | 85.81 | |
| Dealer 2 quote | 85.73 85.75 | ||
| Dealer 3 quote | 85.81 85.83 | ||
| Arbitrage condition | DO L IB | DBi G IO |
If the dealer quote falls entirely to the left of the interbank quote, then the DO L IB condition exists, and an arbitrage profit can be made by buying base currency from the dealer and selling it in the interbank market. On the other hand, if the dealer quote falls entirely to the right of the interbank quote, then the DBi G IO condition exists and an arbitrage profit can be made by buying the base currency in the interbank market and selling it to the dealer. Any other arrangement of the dealer quote will not result in an arbitrage opportunity. Therefore, in our example, dealer 1’s quote doesn’t provide an arbitrage opportunity whereas dealer 2’s quote provides an arbitrage opportunity as the DO L IB condition and dealer 3’s quote provides an arbitrage opportunity as the DBi G IO condition.
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