Unlike stock markets, which can trace their roots back centuries, the forex market as we understand it today is a truly new market. Of course, in its most basic sense—that of people converting one currency to another for financial advantage—forex has been around since nations began minting currencies. But the modern forex markets are a modern invention. After the accord at Bretton Woods in 1971, more major currencies were allowed to float freely against one another. The values of individual currencies vary, which has given rise to the need for foreign exchange services and trading.
The 2nd method is by performing a carry trade, where you can profit by buying a currency with a higher interest rate, and selling a currency with a lower interest rate. An example of this would be the USD/CHF (Swiss franc). If you buy USD/CHF, you are buying the USD, and their interest rates are higher than Swiss interest rates, so if you hold the position overnight, every day you hold the trade you will make money, and the money will be deposited in your brokerage account.
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Since the market is made by each of the participating banks providing offers and bids for a particular currency, the market pricing mechanism is based on supply and demand. Because there are such large trade flows within the system, it is difficult for rogue traders to influence the price of a currency. This system helps create transparency in the market for investors with access to interbank dealing.