Cross Rate

A cross rate is the exchange rate between two currencies derived from their individual rates against a third currency, usually the US dollar. If you want to know how many pounds you get per euro — EUR/GBP — you can calculate it from EUR/USD and USD/GBP without needing a separate market. This is the fundamental principle behind all minor currency pairs.

How a cross rate is calculated

The math is straightforward. If EUR/USD = 1.0850 (one euro costs 1.0850 dollars) and USD/GBP = 0.7920 (one dollar costs 0.7920 pounds), then EUR/GBP = 1.0850 ÷ 0.7920 = 1.3698 pounds per euro. The cross rate is synthetic: it is not traded directly but derived from the two dollar quotes.

This works with any two currencies and any third currency as the base. Historically, before the euro, most cross rates were calculated from gold prices or sterling rates. Today, the dollar is the standard base, but in principle any frequently-quoted currency works.

Who trades cross rates?

Companies with multi-currency exposure — a French firm paying a British supplier, a Japanese exporter selling to Australia — naturally encounter cross rates. It is cheaper to execute EUR/GBP directly than to convert euros to dollars and then dollars to pounds. This created market demand for cross-rate prices.

Banks that make prices on minor currency pairs are not quoting an independent market; they are synthesizing the cross from the dollar pairs and marking it up slightly. The difference between the synthetic rate (calculated from dollar pairs) and the quoted rate (what the bank actually charges) is a small profit margin — typically 1–2 pips of the cross rate’s value.

Bid-ask spreads on crosses

A cross rate’s spread is determined by the spreads of the two component dollar rates. If EUR/USD trades 1 pip bid-ask and GBP/USD trades 1 pip, the EUR/GBP cross will spread roughly 2 pips (the sum of the two component spreads, adjusted for the mathematics of the conversion). This is why minor pairs have wider spreads than major pairs: they inherit the spreads of two major pairs.

Triangular arbitrage

A cross rate that deviates significantly from its theoretical value creates an arbitrage opportunity. If EUR/GBP is trading at 1.3700, but the calculated rate from EUR/USD and GBP/USD is 1.3680, an arbitrageur can buy euros, sell dollars, and buy pounds to lock in the spread. These trades execute instantly, keeping cross rates aligned with their synthetic values. For this reason, cross-rate prices are usually very tight — any deviation is instantly arbitraged away.

Forward cross rates

Forward rates for currency pairs also follow from interest-rate parity. A forward EUR/GBP is derived from the forward EUR/USD, forward GBP/USD, and the interest rates of all three currencies. The calculation is complex but mechanical. Banks construct forward cross-rate prices the same way they construct spot cross-rate prices: synthetically, from the dollar pairs and the interest-rate differentials.

See also