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

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  • Aki-Hiro Sato
  • Hideki Takayasu

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.

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  • Aki-Hiro Sato & Hideki Takayasu, 2001. "Derivation of ARCH(1) process from market price changes based on deterministic microscopic multi-agent," Papers cond-mat/0104313, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0104313
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    References listed on IDEAS

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    1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    2. Bak, P. & Paczuski, M. & Shubik, M., 1997. "Price variations in a stock market with many agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 430-453.
    3. Takayasu, Hideki & Miura, Hitoshi & Hirabayashi, Tadashi & Hamada, Koichi, 1992. "Statistical properties of deterministic threshold elements — the case of market price," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 184(1), pages 127-134.
    4. Sato, Aki-Hiro & Takayasu, Hideki, 1998. "Dynamic numerical models of stock market price: from microscopic determinism to macroscopic randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 231-252.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Deutsch, J.M., 1994. "Probability distributions for one component equations with multiplicative noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 208(3), pages 433-444.
    7. Johnson, N.F. & Jarvis, S. & Jonson, R. & Cheung, P. & Kwong, Y.R. & Hui, P.M., 1998. "Volatility and agent adaptability in a self-organizing market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 258(1), pages 230-236.
    8. Thomas Lux & Michele Marchesi, 1999. "Scaling and criticality in a stochastic multi-agent model of a financial market," Nature, Nature, vol. 397(6719), pages 498-500, February.
    9. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Andreas Krause, 2003. "Inventory Effects on Daily Returns in Financial Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(07), pages 739-765.

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