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Cross rate

By Jarosław Wasiński • Published: • Updated:
An exchange rate calculated using two rates against a common third currency. In market usage, a cross-currency pair often means a pair without USD, such as EUR/GBP. The third currency need not always be USD, and bid/ask sides and transaction costs matter when calculating an executable cross rate.
Example.

Model quotes in USD per unit: EUR/USD 1.1000/1.1002 and GBP/USD 1.2500/1.2503. The synthetic EUR/GBP Bid is 1.1000/1.2503 ≈ 0.879789; Ask is 1.1002/1.2500 = 0.880160 GBP per EUR. These are simultaneous assumed executable quotes, before additional fees and size constraints.

Follow the units and the transaction

Selling EUR for GBP through USD first sells EUR at EUR/USD Bid and then buys GBP at GBP/USD Ask. The ratio gives the cross Bid. Buying EUR reverses the path: EUR/USD Ask divided by GBP/USD Bid gives the cross Ask. Multiplication is appropriate for a different arrangement, such as EUR/USD × USD/JPY, because the USD units cancel.

Direct quotes and synthetic quotes

A directly quoted EUR/GBP market can have different executable prices from the two-leg construction. Credit access, size, fees and quote timing matter. Rates from two unsynchronised chart closes are not evidence that an arbitrage was tradable. Executing one leg while the other fails leaves currency exposure.

Inversion and rounding

For an inverse two-way quotation, new Bid = 1/old Ask and new Ask = 1/old Bid. Preserve sufficient precision during the calculation, then round according to the instrument’s rules. A midpoint-only ratio can explain the unit conversion, but cannot by itself measure the cost of the two actual currency exchanges.

FAQ

Can I divide both Bid prices to obtain the cross Bid?

Not in the EUR/USD and GBP/USD construction above. Selling EUR and buying GBP uses opposite sides of the two quotes.

Must a cross pair trade through USD?

No. A pair can trade directly, and another suitable currency can be used to calculate a synthetic rate.

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Jarosław Wasiński

Editor-in-chief, ForexMechanics.com • Macro & FX analyst

Independent analyst and practitioner with over 20 years of experience in financial markets. Actively involved in Forex since 2007, with a focus on fundamental analysis, OTC market structure, and disciplined capital risk management.

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