Cross Exchange Rate Discrepancies
Triangular arbitrage opportunities may only exist when a bank's quoted exchange rate is not equal to the market's implicit cross exchange rate. The following equation represents the calculation of an implicit cross exchange rate, the exchange rate one would expect in the market as implied from the ratio of two currencies other than the base currency.
where
- is the implicit cross exchange rate for dollars in terms of currency a
- is the quoted market cross exchange rate for b in terms of currency a
- is the quoted market cross exchange rate for dollars in terms of currency b
- is merely the reciprocal exchange rate for currency b in dollar terms, in which case division is used in the calculation
If the market cross exchange rate quoted by a bank is equal to the implicit cross exchange rate as implied from the exchange rates of other currencies, then a no-arbitrage condition is sustained. However, if an inequality exists between the market cross exchange rate, and the implicit cross exchange rate, then there exists an opportunity for arbitrage profits on the difference between the two exchange rates.
Read more about this topic: Triangular Arbitrage
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