Currency is probably one of the most traded product in a day to day basis. International companies are doing business in many countries which also mean there is a disparity between the currency amount in inflow and outflow. Individual investors may also want to exchange their currency to purchase products in another country. In general, investors might be interested to Foreign Exchange Market for speculating on the movement of a specific currency, hedging a position or realizing arbitrage trades.
Before to start discussing about statistical properties of currency or even how to simulate price paths, it is important to understand the structure of Foreign Exchange Market, often called FOREX.
Both financial institutions and banks are referred as “bank” in the above graphic. Those market participants pay monthly fees to access a private network to trade spot currencies provided by either EBS (ICAP) or Reuters (Thomson Reuters). Some currencies are more liquid (higher volume of transaction) in EBS and inversely true with Reuters. Similarly as LIBOR, EBS/ICAP and Reuters electronic platforms are mainly used by banks to trade with each other if there is already a credit agreement between both participant. Usually, the minimum size is one million of the base currency. In brief, the structure may seem similar to typical financial exchange, as CME and Euronext, but the main difference is that credit risks are assumed by every single traders on this market (similarly as Forward contract). In some situation, the best bid price (buyer) may be higher than the best ask price (seller) if there is no credit agreement between them. Readers should consult Forward Vs Futures tutorial if they are not comfortable with these contracts.
In addition of spot currency market previously described, there is also financial markets (CME, Euronext, …) which provide Futures products that replicate fluctuations of the underlying (spot currency). The size of transactions is much smaller than the spot market which make it easier for smaller investors. Note that both individual investors and banks usually trade on these markets.