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Evaluation of Perpetual American Put Options with General Payoff

Author

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  • Luca Anzilli

    (Department of Economic Sciences, University of Salento, 73100 Lecce, Italy)

  • Lucianna Cananà

    (Ionian Department of Law, Economics and Environment, University of Bari “Aldo Moro”, 74121 Taranto, Italy)

Abstract

In this paper, we study perpetual American put options with a generalized standard put payoff and establish sufficient conditions for the existence and uniqueness of the solution to the associated pricing problem. As a key tool, we express the Black–Scholes operator in terms of elasticity. This formulation enables us to demonstrate that the considered pricing problem admits a unique solution when the payoff function exhibits strictly decreasing elasticity with respect to the underlying asset. Furthermore, this approach allows us to derive closed-form solutions for option pricing.

Suggested Citation

  • Luca Anzilli & Lucianna Cananà, 2025. "Evaluation of Perpetual American Put Options with General Payoff," Risks, MDPI, vol. 13(6), pages 1-20, June.
    • Handle: RePEc:gam:jrisks:v:13:y:2025:i:6:p:112-:d:1678169
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    References listed on IDEAS

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    1. Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2021. "Valuation of piecewise linear barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    2. Lee, Jung-Kyung, 2020. "A simple numerical method for pricing American power put options," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Donald Aingworth & Sanjiv Das & Rajeev Motwani, 2006. "A simple approach for pricing equity options with Markov switching state variables," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 95-105.
    4. Gordon Sick & Andrea Gamba, 2010. "Some Important Issues Involving Real Options: An Overview," Multinational Finance Journal, Multinational Finance Journal, vol. 14(1-2), pages 73-123, March-Jun.
    5. Johnson, Paul & Szabó, Dávid Zoltán & Duck, Peter, 2024. "Optimal trading with regime switching: Numerical and analytic techniques applied to valuing storage in an electricity balancing market," European Journal of Operational Research, Elsevier, vol. 319(2), pages 611-624.
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