The market simulates the FX market trading activ­ity on at the level of a market-maker market.

Since the FX market operates continuously 24 hours a day the market applies physical time to account for the different FX market seasonalities. For simplicity of our analysis, we assume that there is only one currency pair (EUR/USD) available for trading in the market.

A currency pair in the market represented as a base and quote in which these two currencies are traded. The bid rate denoted by B_t over the period t at which a trader can sell base currency and buy an equivalent amount of the quoted currency to buy the base currency, go short. Respectively, the ask rate denoted by A_t over the period t is the offer rate at which a trader can buy base currency and sell an equivalent amount of the quoted currency to pay for the base currency, go Long. A currency pair exchange rate at time t is denoted by r(t)=B_t∕A_t.

The market is populated by a number of trad­ing agents that participate in the market in terms of buying and selling currencies. We consider N trading agents divided in N_c counter traders and N_t trend following traders (N = N_c + N_t). We keep N constant at 10⁴ trading agents. A trading agent i is able of holding at any time t in the market:

(a) a risk free asset (cash) denoted by c_i (t), and

(b) a risky asset (currency) denoted by h_i (t), or

(c) both of them. The trading agents are modelled to responds to price changes and events affecting the market. Particularly, they look for detecting periodic patterns in the price fluctuation. A trad­ing agent take a decision d_i (t) at each time step t of the simulation, based on the trading agent budget constraints and preferences. All the market orders placed by the different trading agents will be completely satisfied. However, limit orders will be executed only if the order’s constraints are achieved. At the end of each time step t of the market, the trading agents’ holdings of cash and the risky asset will be updated, based on the currency pair exchange rate r (t) at time t.

There are two basic components, which char­acterize the model; the trading agents’ behaviour and the validation of the trading agents’ collective behaviour in replicating FX market trading activity.

7.1.