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What is a Cross and How do you Derive a Cross Rate?

The US dollar (USD) is the currency against which all other currencies are priced.  Any exchange rate (AUDCAD for instance) that does not involve the USD is considered a “cross rate”.

Currency cross rates are not usually quoted outside of a few significant market pairs: EURGBP, EURJPY, EURCHF and AUDNZD.

 If you are trying to derive the rate at which you would change your base currency and it doesn’t involve USD you may need to find the cross rate. 

In order to do this you have to find two currency pairs: one that contains your home currency and the other must contain the foreign currency that you want to exchange it with.  Then you need to determine what type of quote each of your two selected currency pairs is and apply the corresponding rule for deriving a cross rate.

Direct Quote: 1 foreign currency unit = x home currency units
Indirect Quote: 1 home currency unit = x foreign currency units

How to Derive a Cross Rate from a Direct Quote & Direct Quote:

Rule: divide the terms currency by the base currency on the opposite side

Example: Derive the rate for JPYCAD

BidAsk
USDJPY119.25 119.65 USD is base, JPY is term
USDCAD 1.0485 1.0535 USD is base, CAD is term

The JPYCAD Bid rate
=divide the term currency bid by the base currency ask
=1.0485 / 119.65 = 0.008763

this is the rate at which the market buys JPY and sells CAD

The JPYCAD Ask rate
= divide the term currency ask by the base currency bid
= 1.0535 / 119.25 = 0.008834

this is the rate at which the market sells JPY and buys CAD

How to Derive a Cross Rate for a Direct Quote & Indirect Quote:

Rule: Multiply on the same side

Example: Derive the rate for EURCAD

BidAsk
EURUSD 1.3798 1.3858
USDCAD 1.0432 1.0502
The EURCAD Bid rate
= 1.3798 x 1.0432 = 1.4394

this is the rate at which the market buys EUR and sells CAD

The EURCAD Ask rate
= 1.3858 x 1.0502 = 1.4553

this is the rate at which the market sells EUR and buys CAD

How to Derive a Cross Rate for an Indirect Quote & Indirect Quote:

Rule: Divide the base currency by the terms currency on opposite sides of the spread.

Example: Derive the rate for GBPEUR

BidAsk
GBPUSD 1.9850 1.9950 GBP is base, USD is terms
EURUSD 1.3460 1.3520 EUR is base, USD is terms

The GBPEUR Bid rate
= divide the base currency bid by the terms currency ask
= 1.9850 / 1.3520 = 1.4682

this is the rate at which the market buys GBP and sells EUR at 1.4682 EUR per GBP.

The GBPEUR Ask rate
= divide the base currency ask by the terms currency bid
= 1.9950 / 1.3460 = 1.4821

this is the rate at which the market sells GBP and buys EUR at 1.4821 EUR per

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