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

Aki-Hiro Sato·Hideki Takayasu
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Abstract

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.

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Aki-Hiro Sato, Hideki Takayasu. 2006-12-12. Artificial market model based on deterministic agents and derivation of limit of GARCH type process. https://arxiv.org/abs/cond-mat/0109139

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