Evaluation of Perpetual American Put Options with General Payoff

Luca Anzilli () and Lucianna Cananà
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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

Risks, 2025, vol. 13, issue 6, 1-20

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.

Keywords: perpetual American option; option pricing; non-linear payoff; free-boundary problem; elasticity; power option (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2025
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