Artificial market model based on deterministic agents and derivation of limit of GARCH type process

We investigate the dealer model – an artificial market model based on deterministic agents both numerically and theoretically. The agents refer to the past market prices and changes their ask/bid price. The temporal development of the market price fluctuations is calculated numerically. A probability density function of the market price changes has power law tails. Autocorrelation coefficient of the changes has an anti-correlation, and autocorrelation coefficient of squared changes (volatility correlation function) has a long time correlation. A probability density function of intervals between two successive transactions follows a geometric distribution. The GARCH type stochastic process is approximately derived from the market changes of the model in a limit case. We discuss two factors of the market price fluctuations and display a relation between the volatility of the market prices and a demand-supply curve. We conclude that the ∗Corresponding author. Fax +81-75-753-4919. E-mail address: [email protected] (A.-H. Sato).