Cross rates are rates between two currencies where neither is the US dollar.

A cross rate can be calculated from the respective rate for each of the currencies against the dollar.

Example

Consider the following rates:

USD/SEK   6.6270-6.6275

USD/SGD   1.4143-1.4148

From these rates for the Swedish krona and Singapore dollar against the US dollar, we can calculate a cross rate for the krona against the Singapore dollar.

The first step is to decide which is to be the base currency. Either can be the base currency (and cross rates are published both ways in the financial press, i.e. with each currency as the base). In most cases, however, the market convention is that the currency with the higher value per unit is the base, so that the cross rate will be a number greater than 1 ½ Singapore dollars and over 6 ½ kronas, so the Singapore dollar must have greater unit value than the krona.

We shall therefore take the Singapore Dollar as the base currency to obtain a cross rate for SGD/SEK.

Bid Price

The bid price in the cross rate is the rate at which the market maker will:

• Buy Singapore dollars, and
• Sell kronas

If this transaction were carried out in two stages, via the US dollar, the market maker would:

• Buy Singapore dollars in exchange for US dollars. The USD/SGD rate is 1.4143/48. Since US dollars, the base currency, are being sold, the market maker would quote the offer price 1.4148.
• Sell kronas in exchange for US dollars. The USD/SEK rate is 6.6270/75.Since US dollars (base currency) are being purchased, the market maker would quote the bid price, 6.6270.

The bid price for SGD/SEK is therefore:

\= 6.6270/1.4148 = 4.6841

Offer Price

The offer price in the cross rate is the rate at which the market maker will:

• Sell Singapore dollars, and
• Buy kronas

If this transaction were carried out in two stages via the US dollar, the market maker would:

Sell Singapore dollars and buy US dollars. The USD/SGD rate is 1.4143/48.Since USD is the base, the bid rate of 1.4143 would be quoted

Buy kronas and sell US dollars. The USD/SEK rate is 6.627/75.Since USD is the base, the offer rate of 6.6275 would be quoted.

The offer price for SGD/SEK is therefore:

\= 6.6275/1.4143 = 4.6861

Solution SGC/SEK cross rate

This gives us a cross rate of SGD/SEK 4.6841-4.6861 (4.6841/61).