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Option Pricing with the Logistic Return Distribution

Author

Listed:
  • Haim Levy

    (The Jerusalem School of Business Administration, The Hebrew University of Jerusalem, Jerusalem 91905, Israel)

  • Moshe Levy

    (The Jerusalem School of Business Administration, The Hebrew University of Jerusalem, Jerusalem 91905, Israel)

Abstract

The Black–Scholes model and many of its extensions imply a log-normal distribution of stock total returns over any finite holding period. However, for a holding period of up to one year, empirical stock return distributions (both conditional and unconditional) are not log-normal, but rather much closer to the logistic distribution. This paper derives analytic option pricing formulas for an underlying asset with a logistic return distribution. These formulas are simple and elegant and employ exactly the same parameters as B&S. The logistic option pricing formula fits empirical option prices much better than B&S, providing explanatory power comparable to much more complex models with a larger number of parameters.

Suggested Citation

  • Haim Levy & Moshe Levy, 2024. "Option Pricing with the Logistic Return Distribution," JRFM, MDPI, vol. 17(2), pages 1-17, February.
    • Handle: RePEc:gam:jjrfmx:v:17:y:2024:i:2:p:67-:d:1337024
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    References listed on IDEAS

    as
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    Full references (including those not matched with items on IDEAS)

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