IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-04500953.html

The Brownian Motion in Finance: An Epistemological Puzzle

Author

Listed:
  • Christian Walter

    (LAP - Laboratoire d’anthropologie politique – Approches interdisciplinaires et critiques des mondes contemporains, UMR 8177 - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

Abstract

While in medicine, comparison of the data supplied by a clinical syndrome with the data supplied by the biological system is used to arrive at the most accurate diagnosis, the same cannot be said of financial economics: the accumulation of statistical results that contradict the Brownian hypothesis used in risk modelling, combined with serious empirical problems in the practical implementation of the Black-Scholes-Merton model, the benchmark theory of mathematical finance founded on the Brownian hypothesis, has failed to change the Brownian representation, which has endured for more than fifty years despite the extent of its invalidation by experience. Without any statistical foundations, one mathematical representation (Brownian motion) has become the established approach, acting in the minds of practitioners as a "prenotion" in the sense the word is used by Durkheim (1894), i.e. a "schematic, summary representation" which has produced a kind of spontaneous epistemology. The question arises of the persistence of this mathematical (Brownian) representation, which has been the basis for every financial risk modelling approach: how can its long life be explained? How was this spontaneous epistemology formed, and why did it prove to be so persistent? To address this question and offer an answer, I will test the various dynamics of scientific knowledge used with reference to financial modelling. All these dynamics are specific ways of describing the relationship between knowledge of a phenomenon (here, the representation of a stock market dynamic) and the phenomenon itself (here, stock price fluctuations). First, I show how it is impossible for the positivist approach to solve the financial puzzle. Next, I turn to the three principal postpositivist dynamics, developed by Kuhn, Lakatos and Quine. My objective is to make to speak these representations of science for financial science, in order to reflect on the dominance of the Brownian representation in finance. I will show that none of the epistemologies examined can explain why the Brownian representation continues to be used in mathematical finance research. I shall then propose an alternative hypothesis, concerning a significant pervading mental model that has irrigated both academics and practitioners in the financial sector: the "principle of continuity" introduced into economics by Alfred Marshall in 1890. I consider that this principle of continuity has become a "persistent idea" in the form of a viral approach to representations, and I give this persistent idea the metaphorical name of the "Brownian virus". Then, to explain the spread of this Brownian virus through the financial sector, the contamination of financial practices by this mental representation founded on the principle of continuity, I introduce the concept of the "financial Logos", a discourse that structures practices and organisations, calculations, prudential regulations and accounting standards, leading to a general financialisation of society from the 1980s onwards.

Suggested Citation

  • Christian Walter, 2019. "The Brownian Motion in Finance: An Epistemological Puzzle," Post-Print halshs-04500953, HAL.
    • Handle: RePEc:hal:journl:halshs-04500953
    DOI: 10.1007/s11245-019-09660-7
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-04500953
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-04500953/document
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s11245-019-09660-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. S. James Press, 1967. "A Compound Events Model for Security Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 317-317.
    2. Benoit Mandelbrot, 1967. "The Variation of Some Other Speculative Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 393-393.
    3. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    4. Christian Walter, 2013. "Le modèle de marche au hasard en finance," Post-Print hal-04712454, HAL.
    5. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
    6. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," The Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
    7. J-P. Bouchaud & M. Potters, 2001. "Welcome to a non-Black-Scholes world," Quantitative Finance, Taylor & Francis Journals, vol. 1(5), pages 482-483.
    8. Christian Walter, 2005. "La gestion indicielle et la théorie des moyennes," Revue d'Économie Financière, Programme National Persée, vol. 79(2), pages 113-136.
    9. Donald MacKenzie, 2006. "An Engine, Not a Camera: How Financial Models Shape Markets," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262134608, December.
    10. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    11. Hsieh, David A, 1991. "Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-1877, December.
    12. Brenner, Menachem, 1974. "On the Stability of the Distribution of the Market Component in Stock Price Changes," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(6), pages 945-961, December.
    13. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    14. Ball, Clifford A & Torous, Walter N, 1985. "On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-173, March.
    15. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christian Walter, 2023. "L’introduction de la loi de Pareto dans la modélisation financière," Post-Print halshs-04494659, HAL.

    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. Boudewijn de Bruin & Christian Walter, 2017. "Research Habits in Financial Modelling: The Case of Non-normality of Market Returns in the 1970s and the 1980s," Post-Print hal-04561125, HAL.
    3. Fong, Wai Mun, 1997. "Robust beta estimation: Some empirical evidence," Review of Financial Economics, Elsevier, vol. 6(2), pages 167-186.
    4. Kaehler, Jürgen & Marnet, Volker, 1993. "Markov-switching models for exchange-rate dynamics and the pricing of foreign-currency options," ZEW Discussion Papers 93-03, ZEW - Leibniz Centre for European Economic Research.
    5. Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
    6. Pezzo, Rosanna & Uberti, Mariacristina, 2006. "Approaches to forecasting volatility: Models and their performances for emerging equity markets," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 556-565.
    7. Liu, Yi & Liu, Huifang & Zhang, Lei, 2019. "Modeling and forecasting return jumps using realized variation measures," Economic Modelling, Elsevier, vol. 76(C), pages 63-80.
    8. Eom, Cheoljun & Kaizoji, Taisei & Scalas, Enrico, 2019. "Fat tails in financial return distributions revisited: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    9. Lin, Bing-Huei & Yeh, Shih-Kuo, 2000. "On the distribution and conditional heteroscedasticity in Taiwan stock prices," Journal of Multinational Financial Management, Elsevier, vol. 10(3-4), pages 367-395, December.
    10. Wai Mun Fong, 1997. "Robust beta estimation: Some empirical evidence," Review of Financial Economics, John Wiley & Sons, vol. 6(2), pages 167-186.
    11. Kaehler, Jürgen, 1991. "Modelling and forecasting exchange-rate volatility with ARCH-type models," ZEW Discussion Papers 91-02, ZEW - Leibniz Centre for European Economic Research.
    12. Semei Coronado-Ram'irez & Pedro Celso-Arellano & Omar Rojas, 2014. "Adaptive Market Efficiency of Agricultural Commodity Futures Contracts," Papers 1412.8017, arXiv.org, revised Mar 2015.
    13. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    14. Ladislav Kristoufek, 2018. "Power-law cross-correlations: Issues, solutions and future challenges," Papers 1806.01616, arXiv.org.
    15. 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.
    16. Christensen, Kim & Oomen, Roel C.A. & Podolskij, Mark, 2014. "Fact or friction: Jumps at ultra high frequency," Journal of Financial Economics, Elsevier, vol. 114(3), pages 576-599.
    17. Mr. Noureddine Krichene, 2006. "Recent Dynamics of Crude Oil Prices," IMF Working Papers 2006/299, International Monetary Fund.
    18. B. Wade Brorsen & Seung-Ryong Yang, 1994. "Nonlinear Dynamics And The Distribution Of Daily Stock Index Returns," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 17(2), pages 187-203, June.
    19. Carolyn W. Chang, 1995. "A No-Arbitrage Martingale Analysis For Jump-Diffusion Valuation," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 18(3), pages 351-381, September.
    20. Leisen, Dietmar P. J., 1999. "The random-time binomial model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1355-1386, September.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    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:hal:journl:halshs-04500953. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.