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

Aki-Hiro Sato and Hideki Takayasu

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Abstract: A model of fluctuations in the market price including many deterministic dealers, who predict their buying and selling prices from the latest price change, is developed. We show that price changes of the model is approximated by ARCH(1) process. We conclude that predictions of dealers affected by the past price changes cause the fat tails of probability density function. We believe that this study bridges stochastic processes in econometrics with multi-agent simulation approaches.

Date: 2001-04
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Published in Proceedings of Empirical Science of Financial Fluctuations - Econophysics on the Horizon, (2002), pp. 172--178

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