Cross Rates and Different Base Currencies

If we look at two sets of currency pairs with different base currencies you can still adopt the same procedure to find a cross currency quote, provided that you remember the basics.

For example, suppose cable (GBP/USD) is 1.6175 and USD/CAD 1.3639/42.

We can now find the GBP/CAD cross rate as follows.



GBP will be taken as the base currency for the cross rate quotation

Bid PriceMarket maker buys GBP, sells CAD
Buy GBP, sell USD at 1.6175
Sell CAD, buy USD at 1.3639
Bid price = 1.6175 X 1.3639 =2.2061
Offer PriceMarket maker sells GBP, buys CAD
Sell GBP, buy USD at 1.6178
Buy CAD, sell USD at 1.3642
Offer price =1.6180 X 1.3642=2.2073
Cross rateGBP/CAD rate is 2.2061-2.2073

Notice that in this example, since the GBP/USD rate is quoted with GBP as base, we need to multiply rather than divide to arrive at the cross rate.

Rules for Calculating Cross Rates

Other Aspects of Cross Rates

In making the above calculations, we have used two spreads, representing liquidity and volatility risk in two markets. This spread is not necessary if a position can be covered directly in one market. Spreads will be wider for less-actively traded cross currency pairs, because the market maker will split deals into two dollar positions, with equal and opposite notional dollar values, and cover them in the respective markets.

Most interbank FX transactions do not involve cross rates, i.e. do not involve the exchange of two non-dollar currencies. Some cross rates, however are increasingly traded by banks in addition to US dollar-based rates.

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