Cross rates: how cross currency pairs are priced

What are cross pairs?

A cross currency pair is a pair that does not include the US dollar, such as EUR/GBP, EUR/JPY or GBP/CHF. Its price is called a cross rate.

Most currencies are traded against the USD, and those markets are the deepest. When a bank or broker quotes a pair without the dollar, it can work the price out from the USD quotes of both currencies. If the notation EUR/GBP is new to you, read how to read a currency pair first.

Forex cross pairs are often split into:

• Major crosses: crosses between major currencies, for example EUR/GBP, EUR/JPY and GBP/JPY.
• Exotic crosses: crosses involving a less traded currency, for example a Scandinavian or emerging-market currency against EUR or JPY.

See currency pairs for the wider grouping and currency codes for the ISO codes.

How a cross rate is derived

The method depends on where the USD sits in each quote.

The logic is simple. A unit of EUR buys a certain amount of USD. That USD buys a certain amount of GBP. Chaining the two steps gives the EUR price in GBP. The USD cancels out of the calculation.

The same idea explains rupee crosses. Most local quotes for PKR are built around USD/PKR. A EUR/PKR or GBP/PKR figure is often derived by combining USD/PKR with EUR/USD or GBP/USD. For official reference rates, see SBP exchange rates.

Worked example with the converter

Use the converter below. It converts at the ECB reference rate.

To see a cross rate being built:

1. Enter an amount in EUR and convert it to USD. Note the USD result.
2. Enter that USD result and convert it to GBP. Note the GBP result.
3. Now convert the original EUR amount straight to GBP.

The result of step 3 should match step 2, apart from rounding. Dividing the GBP result by the EUR amount gives the EUR/GBP cross rate. That is the same as dividing the EUR/USD rate by the GBP/USD rate.

ECB reference rates are mid-rates with no spread. They are useful for checking the arithmetic. They are not the prices you would actually get in a market.

Precise definitions: bid, ask and the synthetic spread

Real quotes have a bid (the price at which you can sell) and an ask (the price at which you can buy). See bid and ask for the basics. When a cross is built from USD pairs, each side has to use the price that is less favourable to the trader.

Division case (EUR/GBP from EUR/USD and GBP/USD):

• EUR/GBP bid = EUR/USD bid ÷ GBP/USD ask
• EUR/GBP ask = EUR/USD ask ÷ GBP/USD bid

Multiplication case (EUR/JPY from EUR/USD and USD/JPY):

• EUR/JPY bid = EUR/USD bid × USD/JPY bid
• EUR/JPY ask = EUR/USD ask × USD/JPY ask

Selling EUR for GBP through the dollar means selling EUR for USD at the bid, then buying GBP with that USD at its ask. So the derived ("synthetic") spread contains both component spreads, measured in relative terms.

Why crosses can have wider spreads

• Combined spreads. A synthetic cross carries the costs of both legs.
• Liquidity. Many crosses have less direct trading than the USD majors. Thinner order books mean wider quotes. See liquidity.
• Session timing. Spreads can widen when the main centres for either currency are closed. They also tend to widen around rollover. Compare session overlaps.
• Volatility and news. Market makers widen quotes when either leg moves fast.

Some major crosses, such as EUR/GBP, have their own deep direct market. Their spread can therefore be narrower than the purely synthetic figure. The spread is only one part of the cost. Commission and swap also count; see what is spread and total trading costs.

Risk and the Pakistan context

Cross pairs are not safer or riskier by nature. However, leveraged CFD and forex trading on any pair can lose money fast, and wider spreads add to the cost of every trade.

Pakistani readers should also know the official position:

• On offshore platforms, per the SECP, offshore forex/CFD platforms operate without regulatory approval in Pakistan.
• On remittances, per the SBP, remitting foreign exchange to overseas forex/margin/CFD platforms is not allowed through any payment channel (FERA s.5(1)).

Read law and regulators before opening any account.

Frequent questions

What are cross rates in simple words?

A cross rate is the exchange rate between two currencies, neither of which is the US dollar. It is usually worked out from each currency's rate against the USD.

Is EUR/USD a cross pair?

No. A pair with the USD on either side is a dollar pair. EUR/GBP or EUR/JPY are crosses.

Why does my calculated cross differ from the quoted price?

Your sources may use mid-rates, while dealers quote bid and ask. Timing and rounding also differ. Direct interbank trading can make the quoted price slightly different from the synthetic one.

Do I divide or multiply?

Divide when the USD sits in the same position in both quotes. Multiply when it is the base in one and the quote in the other.

Where can I do other trading calculations?

See the calculators page.