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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. Atmaz, Adem & Basak, Suleyman, 2019. "Option prices and costly short-selling," Journal of Financial Economics, Elsevier, vol. 134(1), pages 1-28.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
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