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Modified Brownian Motion Approach to Modelling Returns Distribution

Author

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  • Gurjeet Dhesi
  • Muhammad Bilal Shakeel
  • Ling Xiao

Abstract

An innovative extension of Geometric Brownian Motion model is developed by incorporating a weighting factor and a stochastic function modelled as a mixture of power and trigonometric functions. Simulations based on this Modified Brownian Motion Model with optimal weighting factors selected by goodness of fit tests, substantially outperform the basic Geometric Brownian Motion model in terms of fitting the returns distribution of historic data price indices. Furthermore we attempt to provide an interpretation of the additional stochastic term in relation to irrational behaviour in financial markets and outline the importance of this novel model.

Suggested Citation

  • Gurjeet Dhesi & Muhammad Bilal Shakeel & Ling Xiao, 2015. "Modified Brownian Motion Approach to Modelling Returns Distribution," Papers 1507.02203, arXiv.org.
    • Handle: RePEc:arx:papers:1507.02203
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    References listed on IDEAS

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    1. 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.
    2. Hiroshi Takahashi & Takao Terano, 2003. "Agent-Based Approach to Investors? Behavior and Asset Price Fluctuation in Financial Markets," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 6(3), pages 1-3.
    3. Dennis Dittrich & Werner Guth & Boris Maciejovsky, 2005. "Overconfidence in investment decisions: An experimental approach," The European Journal of Finance, Taylor & Francis Journals, vol. 11(6), pages 471-491.
    4. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    5. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    6. de Jong,Frank & Rindi,Barbara, 2009. "The Microstructure of Financial Markets," Cambridge Books, Cambridge University Press, number 9780521867849.
    7. Blanchard, Olivier Jean, 1979. "Speculative bubbles, crashes and rational expectations," Economics Letters, Elsevier, vol. 3(4), pages 387-389.
    8. Cappellini, Alessandro & Ferraris, Gianluigi, 2007. "Waiting Times in Simulated Stock Markets," MPRA Paper 7324, University Library of Munich, Germany.
    9. De Bondt, Werner F M & Thaler, Richard H, 1987. "Further Evidence on Investor Overreaction and Stock Market Seasonalit y," Journal of Finance, American Finance Association, vol. 42(3), pages 557-581, July.
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