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Stock Price Processes with Infinite Source Poisson Agents

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  • Mine Caglar

Abstract

We construct a general stochastic process and prove weak convergence results. It is scaled in space and through the parameters of its distribution. We show that our simplified scaling is equivalent to time scaling used frequently. The process is constructed as an integral with respect to a Poisson random measure which governs several parameters of trading agents in the context of stock prices. When the trading occurs more frequently and in smaller quantities, the limit is a fractional Brownian motion. In contrast, a stable Levy motion is obtained if the rate of trading decreases while its effect rate increases.

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  • Mine Caglar, 2011. "Stock Price Processes with Infinite Source Poisson Agents," Papers 1106.6300, arXiv.org.
  • Handle: RePEc:arx:papers:1106.6300
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    1. Giardina, Irene & Bouchaud, Jean-Philippe & M├ęzard, Marc, 2001. "Microscopic models for long ranged volatility correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 28-39.
    2. Bischi, Gian-Italo & Gallegati, Mauro & Gardini, Laura & Leombruni, Roberto & Palestrini, Antonio, 2006. "Herd Behavior And Nonfundamental Asset Price Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 10(04), pages 502-528, September.
    3. Iori, Giulia, 2002. "A microsimulation of traders activity in the stock market: the role of heterogeneity, agents' interactions and trade frictions," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 269-285, October.
    4. He, Xue-Zhong & Westerhoff, Frank H., 2005. "Commodity markets, price limiters and speculative price dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 29(9), pages 1577-1596, September.
    5. Farmer, J. Doyne & Joshi, Shareen, 2002. "The price dynamics of common trading strategies," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 149-171, October.
    6. Cioczek-Georges, R. & Mandelbrot, B. B., 1996. "Alternative micropulses and fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 64(2), pages 143-152, November.
    7. Irene Giardina & Jean-Philippe Bouchaud & Marc Mezard, 2001. "Microscopic models for long ranged volatility correlations," Science & Finance (CFM) working paper archive 500024, Science & Finance, Capital Fund Management.
    8. repec:wsi:ijmpcx:v:13:y:2002:i:01:n:s0129183102003000 is not listed on IDEAS
    9. K. Sznajd-Weron & R. Weron, 2002. "A Simple Model Of Price Formation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 115-123.
    10. D. Challet & A. Chessa & M. Marsili & Y-C. Zhang, 2001. "From Minority Games to real markets," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 168-176.
    11. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2006. "A Limit Theorem for Financial Markets with Inert Investors," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 789-810, November.
    12. Irene Giardina & Jean-Philippe Bouchaud & Marc M'ezard, 2001. "Microscopic Models for Long Ranged Volatility Correlations," Papers cond-mat/0105076, arXiv.org.
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