# How to Calculate the Cross-Exchange Rate

2023-08-03
Summary:

Learn to calculate cross-exchange rates with EBC's comprehensive guide. Understanding exchange rates is crucial for international transactions.

When two currencies do not have a direct exchange rate and must be indirectly calculated through a third currency, the exchange rate is called the cross exchange rate or arbitrage exchange rate. Those without US dollars in a "currency pair" are called crosses, while those with US dollars in a "currency pair" are called direct crosses. By using any two direct exchanges, the exchange rate for a cross exchange can be calculated, which is the cross exchange rate.

This exchange rate is usually used for currency exchange without a direct quotation. Calculating cross-exchange rates requires the following stEPS:

1. Determine the reference currency.

Firstly, determine a reference currency that will be used as the intermediate currency for cross-exchange rate calculations. This is usually a currency widely used internationally, such as the US dollar (USD) or the euro (EUR).

2. Determine the base currency and quotation currency.

Select two currencies for exchange rate calculation, one of which is called the base currency and the other is called the quotation currency.

3. Find the exchange rate between the base currency and the reference currency.

Use direct quotes available in the market to find the exchange rate between the base currency and the reference currency. For example, if the base currency is Japanese yen (JPY) and the reference currency is the US dollar (USD), look up the exchange rate for converting Japanese yen into US dollars.

4. Find the exchange rate between the quotation currency and the reference currency.

Similarly, use direct quotes available in the market to find the exchange rate between the quoted currency and the reference currency. For example, if the quotation currency is the Euro (EUR) and the reference currency is the US dollar (USD), look up the exchange rate for converting the Euro to US dollars.

5. Calculate the cross exchange rate.

Calculate the cross-exchange rate between two currencies using known direct exchange rates. This can be achieved by dividing the exchange rate between the base currency and the reference currency by the exchange rate between the quoted currency and the reference currency. For example, if the exchange rate for converting the base currency from Japanese yen (JPY) to US dollars (USD) is 1 USD = 110 JPY and the exchange rate for converting the quoted currency from euros (EUR) to US dollars (USD) is 1 USD = 0.9 EUR, then the cross exchange rate of 121.11 JPY/EUR can be calculated by calculating 110 JPY = 0.9 EUR.

Calculation formula for the cross-exchange rate

1. Both currency pairs can be calculated using the direct quotation method or the indirect quotation method using exchange rate cross division (i.e., the buying price of one direct order divided by the selling price of the other direct order, and the selling price of one direct order divided by the buying price of the other direct order).

For example, if US dollar/Swiss franc = 1.4000/1.4010 and US dollar/Japanese yen = 123.50/60, how many Japanese yen equal 1 Swiss franc?

Purchase price: 123.5/1.4010 = 88.15 yen = 1 Swiss franc

Selling price: 123.6/1.4 = 88.29 yen = 1 Swiss franc

So CHF/JPY=88.15/88.29

2. If two currencies use the direct quotation method for one and the indirect quotation method for the other, the direct multiplication method is used to calculate (i.e., the buying price of one direct order is multiplied by the buying price of the other direct order, and the selling price of one direct order is multiplied by the selling price of the other direct order).

For example: USD/JPY = 123.50/60; EUR/USD = 1.0510/20; 1 EUR=how much JPY?

Purchase price: 123.5 * 1.0510 = 129.68 yen = 1 euro

Selling price: 123.6 * 1.0520 = 130.03 yen = 1 euro.

So EUR/JPY=129.68/130.03

There may be certain differences in the calculation of cross-exchange rates that are caused by market bias and transaction costs. Therefore, in actual transactions, investors should pay attention to referring to the exchange rates provided by multiple reliable financial institutions or trading platforms to ensure accurate cross-exchange rates. It is recommended to refer to the real-time exchange rates of the day and the information provided by relevant institutions.

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