IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v11y2023i2p24-d1039021.html
   My bibliography  Save this article

A Generalized Model for Pricing Financial Derivatives Consistent with Efficient Markets Hypothesis—A Refinement of the Black-Scholes Model

Author

Listed:
  • Jussi Lindgren

    (Ministry of Finance, 00023 Helsinki, Finland)

Abstract

This research article provides criticism and arguments why the canonical framework for derivatives pricing is incomplete and why the delta-hedging approach is not appropriate. An argument is put forward, based on the efficient market hypothesis, why a proper risk-adjusted discount rate should enter into the Black-Scholes model instead of the risk-free rate. The resulting pricing equation for derivatives and, in particular, the formula for European call options is then shown to depend explicitly on the drift of the underlying asset, which is following a geometric Brownian motion. It is conjectured that with the generalized model, the predicted results by the model could be closer to real data. The adjusted pricing model could partly also explain the mystery of volatility smile. The present model also provides answers to many finance professionals and academics who have been intrigued by the risk-neutral features of the original Black-Scholes pricing framework. The model provides generally different fair values for financial derivatives compared to the Black-Scholes model. In particular, the present model predicts that the original Black-Scholes model tends to undervalue for example European call options.

Suggested Citation

  • Jussi Lindgren, 2023. "A Generalized Model for Pricing Financial Derivatives Consistent with Efficient Markets Hypothesis—A Refinement of the Black-Scholes Model," Risks, MDPI, vol. 11(2), pages 1-5, January.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:2:p:24-:d:1039021
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/11/2/24/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/11/2/24/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. A. James Boness, 1964. "Elements of a Theory of Stock-Option Value," Journal of Political Economy, University of Chicago Press, vol. 72(2), pages 163-163.
    3. Saeed Marzban & Erick Delage & Jonathan Yu-Meng Li, 2022. "Equal risk pricing and hedging of financial derivatives with convex risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 22(1), pages 47-73, January.
    4. Atmaz, Adem & Basak, Suleyman, 2019. "Option prices and costly short-selling," Journal of Financial Economics, Elsevier, vol. 134(1), pages 1-28.
    5. O'Brien, Thomas J & Selby, Michael J P, 1986. "Option Pricing Theory and Asset Expectations: A Review and Discussion in Tribute to James Boness," The Financial Review, Eastern Finance Association, vol. 21(4), pages 399-418, November.
    6. Paul A. Samuelson, 1973. "Proof That Properly Discounted Present Values of Assets Vibrate Randomly," Bell Journal of Economics, The RAND Corporation, vol. 4(2), pages 369-374, Autumn.
    7. 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.
    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. Robert C. Merton, 2006. "Paul Samuelson and Financial Economics," The American Economist, Sage Publications, vol. 50(2), pages 9-31, October.
    2. Alexander S. Sangare, 2005. "Efficience des marchés : un siècle après Bachelier," Revue d'Économie Financière, Programme National Persée, vol. 81(4), pages 107-132.
    3. Peter Cappelli & Martin J. Conyon, 2011. "Stock Option Exercise and Gift Exchange Relationships: Evidence for a Large US Company," NBER Working Papers 16814, National Bureau of Economic Research, Inc.
    4. Nicolas Brisset, 2018. "Models as speech acts: the telling case of financial models," Journal of Economic Methodology, Taylor & Francis Journals, vol. 25(1), pages 21-41, January.
    5. Merton, Robert C., 1993. "On the microeconomic theory of investment under uncertainty," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 13, pages 601-669, Elsevier.
    6. 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.
    7. Brandouy, Olivier & Delahaye, Jean-Paul & Ma, Lin & Zenil, Hector, 2014. "Algorithmic complexity of financial motions," Research in International Business and Finance, Elsevier, vol. 30(C), pages 336-347.
    8. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    9. Peter Cappelli & Martin Conyon & David Almeda, 2020. "Social Exchange and the Effects of Employee Stock Options," ILR Review, Cornell University, ILR School, vol. 73(1), pages 124-152, January.
    10. Thomas Delcey, 2019. "Samuelson vs Fama on the Efficient Market Hypothesis: The Point of View of Expertise [Samuelson vs Fama sur l’efficience informationnelle des marchés financiers : le point de vue de l’expertise]," Post-Print hal-01618347, HAL.
    11. Kartono, Agus & Solekha, Siti & Sumaryada, Tony & Irmansyah,, 2021. "Foreign currency exchange rate prediction using non-linear Schrödinger equations with economic fundamental parameters," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    12. Gustavo Silva Araujo & Ricardo Alves Carmo Ribeiro, 2018. "Is Petrobras Options Market Efficient? A Study Using The Delta-Gamma Neutral Strategy," Anais do XLIV Encontro Nacional de Economia [Proceedings of the 44th Brazilian Economics Meeting] 126, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    13. Klaus Schredelseker, 2012. "Finanzkrise — Mitschuld der Theorie?," Schmalenbach Journal of Business Research, Springer, vol. 64(8), pages 833-845, December.
    14. Timothy Johnson, 2015. "Reciprocity as a Foundation of Financial Economics," Journal of Business Ethics, Springer, vol. 131(1), pages 43-67, September.
    15. Saggese, Pietro & Belmonte, Alessandro & Dimitri, Nicola & Facchini, Angelo & Böhme, Rainer, 2023. "Arbitrageurs in the Bitcoin ecosystem: Evidence from user-level trading patterns in the Mt. Gox exchange platform," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 251-270.
    16. Paulo Ferreira & Éder J.A.L. Pereira & Hernane B.B. Pereira, 2020. "From Big Data to Econophysics and Its Use to Explain Complex Phenomena," JRFM, MDPI, vol. 13(7), pages 1-10, July.
    17. Linnenluecke, Martina K. & Chen, Xiaoyan & Ling, Xin & Smith, Tom & Zhu, Yushu, 2017. "Research in finance: A review of influential publications and a research agenda," Pacific-Basin Finance Journal, Elsevier, vol. 43(C), pages 188-199.
    18. Giuseppe Garofalo, 2014. "Irreducible complexities: from Gödel and Turing to the paradigm of Imperfect Knowledge Economics," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(6), pages 3463-3474, November.
    19. Catania, Leopoldo & Proietti, Tommaso, 2020. "Forecasting volatility with time-varying leverage and volatility of volatility effects," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1301-1317.
    20. Thomas J. Brennan & Andrew W. Lo & Ruixun Zhang, 2018. "Variety Is the Spice of Life: Irrational Behavior as Adaptation to Stochastic Environments," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 1-39, September.

    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:jrisks:v:11:y:2023:i:2:p:24-:d:1039021. 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.