IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2606.20145.html

Trends, Volatility, Correlations, and Critical Phenomena in Financial Markets

Author

Listed:
  • Sara A. Safari
  • Christoph Schmidhuber

Abstract

We forecast future volatilities and correlations of financial markets based on the current trends in these markets. This complements previous work that models future expected returns by a cubic polynomial of the current trend strength. Empirically, we observe that volatilities and correlations tend to increase day after day in times of strong up- or down-trends. This effect is particularly pronounced in down-trends. It can be accurately quantified by quadratic polynomials of today's trend strengths, which refine common mean-reversion models of volatilities and correlations. Our results improve the prediction of market risk by accounting for market trends. They also support a recent proposal to model financial markets by a lattice gas near its critical point.

Suggested Citation

  • Sara A. Safari & Christoph Schmidhuber, 2026. "Trends, Volatility, Correlations, and Critical Phenomena in Financial Markets," Papers 2606.20145, arXiv.org.
    • Handle: RePEc:arx:papers:2606.20145
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2606.20145
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bacry, E. & Delour, J. & Muzy, J.F., 2001. "Modelling financial time series using multifractal random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 84-92.
    2. 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.
    3. Lisa Borland & Jean-Philippe Bouchaud & Jean-Francois Muzy & Gilles Zumbach, 2005. "The Dynamics of Financial Markets -- Mandelbrot's multifractal cascades, and beyond," Papers cond-mat/0501292, arXiv.org.
    4. Menkhoff, Lukas & Sarno, Lucio & Schmeling, Maik & Schrimpf, Andreas, 2012. "Currency momentum strategies," Journal of Financial Economics, Elsevier, vol. 106(3), pages 660-684.
    5. Claude B. Erb & Campbell R. Harvey, 2005. "The Tactical and Strategic Value of Commodity Futures," NBER Working Papers 11222, National Bureau of Economic Research, Inc.
    6. Qian Shen & Andrew C. Szakmary & Subhash C. Sharma, 2007. "An examination of momentum strategies in commodity futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(3), pages 227-256, March.
    7. Sara A. Safari & Christof Schmidhuber, 2025. "Trends and Reversion in Financial Markets on Time Scales from Minutes to Decades," Papers 2501.16772, arXiv.org, revised May 2025.
    8. Safari, Sara A. & Schmidhuber, Christof, 2025. "Trends and reversion in financial markets on time scales from minutes to decades," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 675(C).
    9. J. P. Bouchaud & S. Ciliberti & Y. Lemp'eri`ere & A. Majewski & P. Seager & K. Sin Ronia, 2017. "Black was right: Price is within a factor 2 of Value," Papers 1711.04717, arXiv.org, revised Nov 2017.
    10. Y. Lemp'eri`ere & C. Deremble & P. Seager & M. Potters & J. P. Bouchaud, 2014. "Two centuries of trend following," Papers 1404.3274, arXiv.org.
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. Gourieroux, Christian & Jasiak, Joann, 2006. "Multivariate Jacobi process with application to smooth transitions," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 475-505.
    13. 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.
    14. Miffre, Joelle & Rallis, Georgios, 2007. "Momentum strategies in commodity futures markets," Journal of Banking & Finance, Elsevier, vol. 31(6), pages 1863-1886, June.
    15. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    16. Lisa Borland & Jean-Philippe Bouchaud & Jean-Francois Muzy & Gilles Zumbach, 2005. "The Dynamics of Financial Markets -- Mandelbrot's multifractal cascades, and beyond," Science & Finance (CFM) working paper archive 500061, Science & Finance, Capital Fund Management.
    17. Sara A. Safari & Maximilian Janisch & Thomas Leh'ericy, 2025. "International Financial Markets Through 150 Years: Evaluating Stylized Facts," Papers 2504.08611, arXiv.org.
    18. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    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. Safari, Sara A. & Schmidhuber, Christof, 2025. "Trends and reversion in financial markets on time scales from minutes to decades," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 675(C).
    2. Schmidhuber, Christof, 2025. "Critical dynamics of random surfaces: Time evolution of area and genus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 678(C).
    3. Schmidhuber, Christof, 2021. "Trends, reversion, and critical phenomena in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    4. Alexandre Subbotin, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 15(3), pages 94-138.
    5. Marco Gregnanin & Johannes De Smedt & Giorgio Gnecco & Maurizio Parton, 2026. "A Generative Adversarial Graph Neural Network for Synthetic Time Series Data," Papers 2605.22215, arXiv.org.
    6. Oussama Tilfani & My Youssef El Boukfaoui, 2020. "Multifractal Analysis of African Stock Markets During the 2007–2008 US Crisis," Review of Pacific Basin Financial Markets and Policies (RPBFMP), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-31, January.
    7. Abdulrahman Alswaidan & Jeffrey D. Varner, 2026. "Hybrid Hidden Markov Model for Modeling Equity Excess Growth Rate Dynamics: A Discrete-State Approach with Jump-Diffusion," Papers 2603.10202, arXiv.org, revised Apr 2026.
    8. Giulia Di Nunno & Kk{e}stutis Kubilius & Yuliya Mishura & Anton Yurchenko-Tytarenko, 2023. "From constant to rough: A survey of continuous volatility modeling," Papers 2309.01033, arXiv.org, revised Aug 2025.
    9. Inoua, Sabiou M. & Smith, Vernon L., 2023. "A classical model of speculative asset price dynamics," Journal of Behavioral and Experimental Finance, Elsevier, vol. 37(C).
    10. Jaume Masoliver & Josep Perello, 2006. "Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 423-433.
    11. Christof Schmidhuber, 2020. "Trends, Reversion, and Critical Phenomena in Financial Markets," Papers 2006.07847, arXiv.org, revised Dec 2020.
    12. Giacomo Bormetti & Sofia Cazzaniga, 2014. "Multiplicative noise, fast convolution and pricing," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 481-494, March.
    13. Achim BACKHAUS & Aliya ZHAKANOVA ISIKSAL, 2016. "The Impact of Momentum Factors on Multi Asset Portfolio," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 146-169, December.
    14. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, January.
    15. Alexander Subbotin & Thierry Chauveau & Kateryna Shapovalova, 2009. "Volatility Models: from GARCH to Multi-Horizon Cascades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390636, HAL.
    16. Qi Xu & Ying Wang, 2021. "Managing volatility in commodity momentum," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(5), pages 758-782, May.
    17. Schmidhuber, Christof, 2022. "Financial markets and the phase transition between water and steam," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 592(C).
    18. Bernardo Spagnolo & Davide Valenti, 2008. "Volatility Effects on the Escape Time in Financial Market Models," Papers 0810.1625, arXiv.org.
    19. Stephen A. Gorman & Frank J. Fabozzi, 2021. "The ABC’s of the alternative risk premium: academic roots," Journal of Asset Management, Palgrave Macmillan, vol. 22(6), pages 405-436, October.
    20. Sara A. Safari & Christof Schmidhuber, 2025. "Trends and Reversion in Financial Markets on Time Scales from Minutes to Decades," Papers 2501.16772, arXiv.org, revised May 2025.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:arx:papers:2606.20145. 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: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    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.