Evaluation of Perpetual American Put Options with General Payoff

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 form...

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Main Authors: Luca Anzilli, Lucianna Cananà
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Risks
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Online Access:https://www.mdpi.com/2227-9091/13/6/112
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author Luca Anzilli
Lucianna Cananà
author_facet Luca Anzilli
Lucianna Cananà
author_sort Luca Anzilli
collection DOAJ
description 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.
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spelling doaj-art-a5bee5e02f3e48249f5838475243a0fb2025-08-20T03:27:32ZengMDPI AGRisks2227-90912025-06-0113611210.3390/risks13060112Evaluation of Perpetual American Put Options with General PayoffLuca Anzilli0Lucianna Cananà1Department of Economic Sciences, University of Salento, 73100 Lecce, ItalyIonian Department of Law, Economics and Environment, University of Bari “Aldo Moro”, 74121 Taranto, ItalyIn 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.https://www.mdpi.com/2227-9091/13/6/112perpetual American optionoption pricingnon-linear payofffree-boundary problemelasticitypower option
spellingShingle Luca Anzilli
Lucianna Cananà
Evaluation of Perpetual American Put Options with General Payoff
Risks
perpetual American option
option pricing
non-linear payoff
free-boundary problem
elasticity
power option
title Evaluation of Perpetual American Put Options with General Payoff
title_full Evaluation of Perpetual American Put Options with General Payoff
title_fullStr Evaluation of Perpetual American Put Options with General Payoff
title_full_unstemmed Evaluation of Perpetual American Put Options with General Payoff
title_short Evaluation of Perpetual American Put Options with General Payoff
title_sort evaluation of perpetual american put options with general payoff
topic perpetual American option
option pricing
non-linear payoff
free-boundary problem
elasticity
power option
url https://www.mdpi.com/2227-9091/13/6/112
work_keys_str_mv AT lucaanzilli evaluationofperpetualamericanputoptionswithgeneralpayoff
AT luciannacanana evaluationofperpetualamericanputoptionswithgeneralpayoff