A numerical model for the foreign exchange (FX) market is developed and its implementation on a distributed memory parallel computer is discussed. The model considers a description of the market at the level of the real agents, such as traders and market makers. These actors are represented by interacting computerized agents. Parallelism allows the study of systems with many actors and realistic trading rules. In order to analyse the generic dynamical properties of the market, simulations are considered. The results agree with several observed features of the real market, such as non-Gaussian distribution and negative short-term autocorrelation of price changes.