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Evaluation of Perpetual American Put Options with General Payoff

Author

Listed:
  • 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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