Artificial market model based on deterministic agents and derivation of limit of GARCH type process
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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.
25 pages, 1 table and 16 figures
25 pages, 1 table and 16 figures