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Explicit Formulas for Hedging Parameters of Perpetual American Options with General Payoffs: A Mellin Transform Approach

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  • Stefan Zecevic

    (School of Mathematics and Applied Statistics, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia
    These authors contributed equally to this work.)

  • Mariano Rodrigo

    (School of Mathematics and Applied Statistics, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia
    These authors contributed equally to this work.)

Abstract

Risk is often the most concerning factor in financial transactions. Option Greeks provide valuable insights into the risks inherent in option trading and serve as tools for risk mitigation. Traditionally, scholars compute option Greeks through extensive calculations. This article introduces an alternative method that bypasses conventional derivative computation using the Mellin transform and its properties. Specifically, we derive Greeks for perpetual American options with general payoffs, represented as piecewise linear functions, and examine higher-order risk metrics for practical implications. Examples are provided to illustrate the effectiveness of our approach, offering a novel perspective on calculating and interpreting option Greeks.

Suggested Citation

  • Stefan Zecevic & Mariano Rodrigo, 2025. "Explicit Formulas for Hedging Parameters of Perpetual American Options with General Payoffs: A Mellin Transform Approach," Mathematics, MDPI, vol. 13(3), pages 1-37, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:479-:d:1581067
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    References listed on IDEAS

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