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A model of fluctuations in the market price including many deterministicdealers, who predict their buying and selling prices from the latest pricechange, is developed. We show that price changes of the model is approximatedby ARCH(1) process. We conclude that predictions of dealers affected by thepast price changes cause the fat tails of probability density function. Webelieve that this study bridges stochastic processes in econometrics withmulti-agent simulation approaches.

Derivation of ARCH(1) process from market price changes based on deterministic microscopic multi-agent