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Daily and Weekly Geometric Brownian Motion Stock Index Forecasts

Author

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  • Amit Sinha

    (Department of Economics and Finance, Foster College of Business at Bradley University, Peoria, IL 61625, USA)

Abstract

In this manuscript, daily and weekly geometric Brownian motion forecasts are obtained and tested for reliability for three indexes, DJIA, NASDAQ and S&P 500. A twenty-year rolling window is used to estimate the drift and diffusion components, and applied to obtain one-period-ahead geometric Brownian motion index values and associated probabilities. Expected values are estimated by totaling up the product of the index value and its associated probabilities, and test for reliability. The results indicate that geometric Brownian-simulated expected index values estimated using one thousand simulations can be reliable forecasts of the actual index values. Expected values estimated using one or ten simulations are not as reliable, while those obtained using at least one hundred simulations could be useful.

Suggested Citation

  • Amit Sinha, 2024. "Daily and Weekly Geometric Brownian Motion Stock Index Forecasts," JRFM, MDPI, vol. 17(10), pages 1-22, September.
    • Handle: RePEc:gam:jjrfmx:v:17:y:2024:i:10:p:434-:d:1488361
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    References listed on IDEAS

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    1. G. P. Nason & R. Von Sachs & G. Kroisandt, 2000. "Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 271-292.
    2. Dash, M., 2019. "Testing the Random Walk Hypothesis in the Indian Stock Market Using ARIMA Modelling," Journal of Applied Management and Investments, Department of Business Administration and Corporate Security, International Humanitarian University, vol. 8(2), pages 71-77, May.
    3. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    4. Jingzhi Tie & Hanqin Zhang & Qing Zhang, 2018. "An Optimal Strategy for Pairs Trading Under Geometric Brownian Motions," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 654-675, November.
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