IDEAS home Printed from https://ideas.repec.org/a/gam/jjrfmx/v17y2024i10p434-d1488361.html
   My bibliography  Save this article

Daily and Weekly Geometric Brownian Motion Stock Index Forecasts

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1911-8074/17/10/434/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1911-8074/17/10/434/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Amit K. Sinha, 2021. "The reliability of geometric Brownian motion forecasts of S&P500 index values," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1444-1462, December.
    2. Schroeder, Anna Louise & Fryzlewicz, Piotr, 2013. "Adaptive trend estimation in financial time series via multiscale change-point-induced basis recovery," LSE Research Online Documents on Economics 54934, London School of Economics and Political Science, LSE Library.
    3. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    4. Athanasia Gavala & Nikolay Gospodinov & Deming Jiang, 2006. "Forecasting volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 381-400.
    5. Asai, Manabu & McAleer, Michael, 2015. "Leverage and feedback effects on multifactor Wishart stochastic volatility for option pricing," Journal of Econometrics, Elsevier, vol. 187(2), pages 436-446.
    6. Söderlind, Paul, 2009. "The C-CAPM without ex post data," Journal of Macroeconomics, Elsevier, vol. 31(4), pages 721-729, December.
    7. Damir Filipovi'c & Martin Larsson, 2017. "Polynomial Jump-Diffusion Models," Papers 1711.08043, arXiv.org, revised Jul 2019.
    8. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    9. Bloom, Nicholas & Bunn, Philip & Chen, Scarlet & Mizen, Paul & Smietanka, Pawel & Thwaites, Gregory, 2019. "The impact of Brexit on UK firms," Bank of England working papers 818, Bank of England.
    10. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    11. Yun, Jaeho, 2014. "Out-of-sample density forecasts with affine jump diffusion models," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 74-87.
    12. Carvalho, Augusto & Guimaraes, Bernardo, 2018. "State-controlled companies and political risk: Evidence from the 2014 Brazilian election," Journal of Public Economics, Elsevier, vol. 159(C), pages 66-78.
    13. Jurczenko, Emmanuel & Maillet, Bertrand & Negrea, Bogdan, 2002. "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)," LSE Research Online Documents on Economics 24950, London School of Economics and Political Science, LSE Library.
    14. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    15. Peng He, 2012. "Option Portfolio Value At Risk Using Monte Carlo Simulation Under A Risk Neutral Stochastic Implied Volatility Model," Global Journal of Business Research, The Institute for Business and Finance Research, vol. 6(5), pages 65-72.
    16. Martin Melecky, 2012. "Choosing The Currency Structure Of Foreign‐Currency Debt: A Review Of Policy Approaches," Journal of International Development, John Wiley & Sons, Ltd., vol. 24(2), pages 133-151, March.
    17. Chang, Eric C. & Ren, Jinjuan & Shi, Qi, 2009. "Effects of the volatility smile on exchange settlement practices: The Hong Kong case," Journal of Banking & Finance, Elsevier, vol. 33(1), pages 98-112, January.
    18. José Valentim Machado Vicente & Jaqueline Terra Moura Marins, 2019. "A Volatility Smile-Based Uncertainty Index," Working Papers Series 502, Central Bank of Brazil, Research Department.
    19. Rui Vilela Mendes & M. J. Oliveira, 2006. "A data-reconstructed fractional volatility model," Papers math/0602013, arXiv.org, revised Jun 2007.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jjrfmx:v:17:y:2024:i:10:p:434-:d:1488361. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.