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The Journal of Derivatives

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The Premium Reduction of European, American, and Perpetual Log Return Options

Stephen Taylor and Jan Vecer
The Journal of Derivatives Summer 2021, jod.2020.1.115; DOI: https://doi.org/10.3905/jod.2020.1.115
Stephen Taylor
is an assistant professor of finance and chair of the fintech and data analysis department of the Martin Tuchman School of Management in the New Jersey Institute of Technology in Newark, New Jersey
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Jan Vecer
is a professor in the department of probability and mathematical statistics at Charles University in Prague, Czech Republic
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Abstract

Traditional plain vanilla options may be regarded as contingent claims whose value depends upon the simple returns of an underlying asset. These options have convex payoffs and as a consequence of Jensen’s inequality, their prices increase as a function of maturity in the absence of interest rates. This results in long dated call option premia being excessively expensive in relation to the fraction of a corresponding insured portfolio. We show that replacing the simple return payoff with the log return call option payoff leads to substantial premium savings, while simultaneous providing the similar insurance protection. Call options on log returns have favorable prices for very long maturities on the scale of decades. This property enables them to be attractive securities for long-term investors, such as pension funds.

TOPICS: Options, Pension funds

Key Findings

  • ▪ This article develops valuation and risk techniques for a log return payoff option under a Geometric Brownian Motion.

  • ▪ Compares premium advantages of the log return contract to those of traditional European options.

  • ▪ Derives a pricing and optimal excise boundary formula for perpetual and finite maturity American log return options.

  • ▪ Examines long-term insurance applications of the new contract that are prohibitively expensive for traditional options.

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The Journal of Derivatives: 29 (5)
The Journal of Derivatives
Vol. 29, Issue 5
Summer 2022
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The Premium Reduction of European, American, and Perpetual Log Return Options
Stephen Taylor, Jan Vecer
The Journal of Derivatives Nov 2020, jod.2020.1.115; DOI: 10.3905/jod.2020.1.115

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The Premium Reduction of European, American, and Perpetual Log Return Options
Stephen Taylor, Jan Vecer
The Journal of Derivatives Nov 2020, jod.2020.1.115; DOI: 10.3905/jod.2020.1.115
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  • Article
    • Abstract
    • MOTIVATION FOR LOG OPTION CONTRACT
    • EUROPEAN LOG CALL OPTION PRICING FORMULA
    • AMERICAN PERPETUAL LOG CALL OPTIMAL DECISION BOUNDARY
    • CONTRACT PROPERTIES AND ITS APPEAL TO CONSERVATIVE INVESTORS
    • APPLICATIONS IN EQUITY MARKETS
    • CONCLUSIONS AND EXTENSIONS
    • ACKNOWLEDGEMENTS
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