  We propose an artificial market model based on deterministic agents. The
agents modify their ask/bid price depending on past price changes. The temporal
development of market price fluctuations is calculated numerically. A
probability density function of 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 successive trading follows a geometric distribution. GARCH
type stochastic process is theoretically derived from this market model in a
limit case. We discuss factors of the market price fluctuations and a relation
between the volatility of the market prices and a demand-supply curve. We
conclude that the power law tails and the long time volatility result from
mechanism of the GARCH type stochastic process.
