Option Pricing with the Logistic Return Distribution

Haim Levy () and Moshe Levy
Additional contact information
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

JRFM, 2024, vol. 17, issue 2, 1-17

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.

Keywords: option pricing; distribution of returns; logistic distribution; holding period (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/1911-8074/17/2/67/pdf (application/pdf)
https://www.mdpi.com/1911-8074/17/2/67/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jjrfmx:v:17:y:2024:i:2:p:67-:d:1337024

Access Statistics for this article

JRFM is currently edited by Ms. Chelthy Cheng

More articles in JRFM from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().