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Simplified Option Price Derivations

David C. Shimko
The Journal of Derivatives Summer 2022, 29 (5) 9-19; DOI: https://doi.org/10.3905/jod.2022.1.160
David C. Shimko
is an industry full professor of financial engineering in the Department of Finance and Risk Engineering at New York University Tandon School of Engineering in Brooklyn, NY
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Abstract

Previous academic research reveals that mean-variance asset pricing (MVAP) models such as the single-period capital asset pricing model (CAPM) fail to produce rational European option prices. This article shows two adaptations of MVAP models that may be used to value derivatives with nonlinear payouts. The first removes static option arbitrage in investors’ optimized aggregate portfolio selection. The second linearizes the pricing kernel, using a static version of the self-financing condition applied in dynamic option modeling. Both adaptations produce risk-neutral derivative prices in equilibrium for all finite-moment probability distributions of underlying asset prices with compact support. The derivation does not require stochastic calculus, frictionless continuous trading assumptions, or the solution of differential equations. The resulting model is a hybrid of equilibrium and arbitrage techniques that rationally values assets and derivatives.

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The Journal of Derivatives: 29 (5)
The Journal of Derivatives
Vol. 29, Issue 5
Summer 2022
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Simplified Option Price Derivations
David C. Shimko
The Journal of Derivatives May 2022, 29 (5) 9-19; DOI: 10.3905/jod.2022.1.160

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Simplified Option Price Derivations
David C. Shimko
The Journal of Derivatives May 2022, 29 (5) 9-19; DOI: 10.3905/jod.2022.1.160
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  • Article
    • Abstract
    • REVIEW OF THE MVAP MODEL: IMPLICATION FOR RELATIVE PRICING
    • OPTION PRICING BY NO-ARBITRAGE IN THE MVAP MODEL
    • DERIVATIVE PRICING USING SELF-FINANCING OR LINEARIZATION
    • CONCLUSION
    • ACKNOWLEDGMENTS
    • ENDNOTES
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