IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2403.19502.html
   My bibliography  Save this paper

On the potential of quantum walks for modeling financial return distributions

Author

Listed:
  • Stijn De Backer
  • Luis E. C. Rocha
  • Jan Ryckebusch
  • Koen Schoors

Abstract

Accurate modeling of the temporal evolution of asset prices is crucial for understanding financial markets. We explore the potential of discrete-time quantum walks to model the evolution of asset prices. Return distributions obtained from a model based on the quantum walk algorithm are compared with those obtained from classical methodologies. We focus on specific limitations of the classical models, and illustrate that the quantum walk model possesses great flexibility in overcoming these. This includes the potential to generate asymmetric return distributions with complex market tendencies and higher probabilities for extreme events than in some of the classical models. Furthermore, the temporal evolution in the quantum walk possesses the potential to provide asset price dynamics.

Suggested Citation

  • Stijn De Backer & Luis E. C. Rocha & Jan Ryckebusch & Koen Schoors, 2024. "On the potential of quantum walks for modeling financial return distributions," Papers 2403.19502, arXiv.org, revised Dec 2024.
    • Handle: RePEc:arx:papers:2403.19502
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2403.19502
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. J. Doyne Farmer & Fabrizio Lillo, 2003. "On the origin of power law tails in price fluctuations," Papers cond-mat/0309416, arXiv.org, revised Jan 2004.
    2. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    3. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    4. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    5. Ewa A. Drzazga-Szczc{e}'sniak & Piotr Szczepanik & Adam Z. Kaczmarek & Dominik Szczc{e}'sniak, 2023. "Entropy of financial time series due to the shock of war," Papers 2303.16155, arXiv.org.
    6. Romanelli, Alejandro & Hernández, Guzmán, 2011. "Quantum walks: Decoherence and coin-flipping games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(6), pages 1209-1220.
    7. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    8. repec:pri:cepsud:91malkiel is not listed on IDEAS
    9. Y. Malevergne & V. Pisarenko & D. Sornette, 2005. "Empirical distributions of stock returns: between the stretched exponential and the power law?," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 379-401.
    10. J. Doyne Farmer, 2000. "Physicists Attempt To Scale The Ivory Towers Of Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 311-333.
    11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    12. Orrell, David, 2020. "A quantum model of supply and demand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    13. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2003. "A theory of power-law distributions in financial market fluctuations," Nature, Nature, vol. 423(6937), pages 267-270, May.
    14. Tuncay, Çağlar & Stauffer, Dietrich, 2007. "Power laws and Gaussians for stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 325-330.
    15. Rama Cont, 2007. "Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 289-309, Springer.
    16. Rostek, S. & Schöbel, R., 2013. "A note on the use of fractional Brownian motion for financial modeling," Economic Modelling, Elsevier, vol. 30(C), pages 30-35.
    17. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    18. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    19. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    20. Plerou, Vasiliki & Gopikrishnan, Parameswaran & Rosenow, Bernd & Amaral, Luis A.N. & Stanley, H.Eugene, 2000. "Econophysics: financial time series from a statistical physics point of view," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 279(1), pages 443-456.
    21. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 59-82, Winter.
    22. Ebrahimi, Nader & Maasoumi, Esfandiar & Soofi, Ehsan S., 1999. "Ordering univariate distributions by entropy and variance," Journal of Econometrics, Elsevier, vol. 90(2), pages 317-336, June.
    23. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    24. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    25. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    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. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    2. Kostanjcar, Zvonko & Jeren, Branko & Juretic, Zeljan, 2012. "Impact of uncertainty in expected return estimation on stock price volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5563-5571.
    3. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    4. Suárez-García, Pablo & Gómez-Ullate, David, 2013. "Scaling, stability and distribution of the high-frequency returns of the Ibex35 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1409-1417.
    5. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    6. Pernagallo, Giuseppe & Torrisi, Benedetto, 2020. "Blindfolded monkeys or financial analysts: Who is worth your money? New evidence on informational inefficiencies in the U.S. stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    7. Roland Rothenstein, 2018. "Quantification of market efficiency based on informational-entropy," Papers 1812.02371, arXiv.org.
    8. Lux, Thomas & Alfarano, Simone, 2016. "Financial power laws: Empirical evidence, models, and mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 3-18.
    9. Christopher M Wray & Steven R Bishop, 2016. "A Financial Market Model Incorporating Herd Behaviour," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-28, March.
    10. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    11. Shu-Heng Chen & Sai-Ping Li, 2011. "Econophysics: Bridges over a Turbulent Current," Papers 1107.5373, arXiv.org.
    12. Thomas Holtfort, 2019. "From standard to evolutionary finance: a literature survey," Management Review Quarterly, Springer, vol. 69(2), pages 207-232, June.
    13. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.
    14. Derksen, M. & Kleijn, B. & de Vilder, R., 2022. "Heavy tailed distributions in closing auctions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    15. Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Eugene Stanley, H., 2008. "Quantifying and understanding the economics of large financial movements," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 303-319, January.
    16. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    17. McCulloch, James, 2012. "Fractal market time," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 686-701.
    18. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(2), pages 461-504.
    19. Sabiou M. Inoua, 2020. "News-Driven Expectations and Volatility Clustering," JRFM, MDPI, vol. 13(1), pages 1-14, January.
    20. James McCulloch, 2012. "Fractal Market Time," Research Paper Series 311, Quantitative Finance Research Centre, University of Technology, Sydney.

    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:2403.19502. 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: http://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.