The main participants in this market are the larger international banks. Financial centers around the world function as anchors of trading between a wide range of multiple types of buyers and sellers around the clock, with the exception of weekends. Since currencies are always traded in pairs, the foreign exchange market does not set a currency's absolute value but rather determines its relative value by setting the market price of one currency if paid for with another. Ex: US$1 is worth X CAD, or CHF, or JPY, etc.
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These cover the bulk of countries outside Europe. Forex brokers catering for India, Hong Kong, Qatar etc are likely to have regulation in one of the above, rather than every country they support. Some brands are regulated across the globe (one is even regulated in 5 continents). Some bodies issue licenses, and others have a register of legal firms.
Forex is a portmanteau of foreign currency and exchange. Foreign exchange is the process of changing one currency into another currency for a variety of reasons, usually for commerce, trading, or tourism. According to a recent triennial report from the Bank for International Settlements (a global bank for national central banks), the average was more than $5.1 trillion in daily forex trading volume.