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
| Bid | Ask | ||
|---|---|---|---|
| USDJPY | 119.25 | 119.65 | USD is base, JPY is term |
| USDCAD | 1.0485 | 1.0535 | USD is base, CAD is term |
=1.0485 / 119.65 = 0.008763
this is the rate at which the market buys JPY and sells CAD
= 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
| Bid | Ask | ||
|---|---|---|---|
| EURUSD | 1.3798 | 1.3858 | |
| USDCAD | 1.0432 | 1.0502 |
this is the rate at which the market buys EUR and sells CAD
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
| Bid | Ask | ||
|---|---|---|---|
| GBPUSD | 1.9850 | 1.9950 | GBP is base, USD is terms |
| EURUSD | 1.3460 | 1.3520 | EUR is base, USD is terms |
= 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.
= 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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